Welcome to Finite Element Methods
The idea for an online version of Finite Element Methods first came a little more than a year ago. Articles about Massively Open Online Classes (MOOCs) had been rocking the academic world (at least gently), and it seemed that your writer had scarcely experimented with teaching methods. Particularly compelling was the fact that there already had been some successes reported with computer programming classes in the online format, especially as MOOCs. Finite Element Methods, with the centrality that computer programming has to the teaching of this topic, seemed an obvious candidate for experimentation in the online format. From there to the video lectures that you are about to view took nearly a year. I first had to take a detour through another subject, Continuum Physics, for which video lectures also are available, and whose recording in this format served as a trial run for the present series of lectures on Finite Element Methods.
Here they are then, about 50 hours of lectures covering the material I normally teach in an introductory graduate class at University of Michigan. The treatment is mathematical, which is natural for a topic whose roots lie deep in functional analysis and variational calculus. It is not formal, however, because the main goal of these lectures is to turn the viewer into a competent developer of finite element code. We do spend time in rudimentary functional analysis, and variational calculus, but this is only to highlight the mathematical basis for the methods, which in turn explains why they work so well. Much of the success of the Finite Element Method as a computational framework lies in the rigor of its mathematical foundation, and this needs to be appreciated, even if only in the elementary manner presented here. A background in PDEs and, more importantly, linear algebra, is assumed, although the viewer will find that we develop all the relevant ideas that are needed.
The development itself focuses on the classical forms of partial differential equations (PDEs): elliptic, parabolic and hyperbolic. At each stage, however, we make numerous connections to the physical phenomena represented by the PDEs. For clarity we begin with elliptic PDEs in one dimension (linearized elasticity, steady state heat conduction and mass diffusion). We then move on to three dimensional elliptic PDEs in scalar unknowns (heat conduction and mass diffusion), before ending the treatment of elliptic PDEs with three dimensional problems in vector unknowns (linearized elasticity). Parabolic PDEs in three dimensions come next (unsteady heat conduction and mass diffusion), and the lectures end with hyperbolic PDEs in three dimensions (linear elastodynamics). Interspersed among the lectures are responses to questions that arose from a small group of graduate students and postdoctoral scholars who followed the lectures live. At suitable points in the lectures, we interrupt the mathematical development to lay out the code framework, which is entirely open source, and C++ based.
It is hoped that these lectures on Finite Element Methods will complement the series on Continuum Physics to provide a point of departure from which the seasoned researcher or advanced graduate student can embark on work in (continuum) computational physics.
There are a number of people that I need to thank: Shiva Rudraraju and Greg Teichert for their work on the coding framework, Tim O'Brien for organizing the recordings, Walter Lin and Alex Hancook for their camera work and postproduction editing, and Scott Mahler for making the studios available.
Krishna Garikipati
Ann Arbor, December 2013
About the Creators
Krishna Garikipati
Dr. Garikipati's work draws from nonlinear mechanics, materials physics, applied mathematics and numerical methods. He's particularly interested in problems of mathematical biology, biophysics and the materials physics. Current research interests include: (1) mathematical and physical modelling of tumor growth, (2) cell mechanics (3) chemomechanically driven phenomena in materials, such as phase transformations and stressinfluenced mass transport. more...
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03.08ct. Coding Assignment 01 
Krishna Garikipati


03.08ct. Coding Assignment 01 Template 
Krishna Garikipati


08.02ct. Coding Assignment 02 
Krishna Garikipati


08.02ct. Coding Assignment 02 Template 
Krishna Garikipati


10.14ct. 1. Coding Assignment 03 
Krishna Garikipati


10.14ct. 1. Coding Assignment 03 Template 
Krishna Garikipati


11.09ct. 1. Coding Assignment 04 
Krishna Garikipati


11.09ct. 1. Coding Assignment 04 Template 
Krishna Garikipati

Document Title  Creator  Downloads  License 

01.01. Introduction. Linear elliptic partial differential equations  I (14:46) 
Krishna Garikipati


01.02. Introduction. Linear elliptic partial differential equations  II (13:01) 
Krishna Garikipati


01.03. Boundary conditions (22:18) 
Krishna Garikipati


01.04. Constitutive relations (20:06) 
Krishna Garikipati


01.05. Strong form of the partial differential equation. Analytic solution (22:44) 
Krishna Garikipati


01.06. Weak form of the partial differential equation  I (12:29) 
Krishna Garikipati


01.07. Weak form of the partial differential equation  II (15:05) 
Krishna Garikipati


01.08. Equivalence between the strong and weak forms  1 (25:10) 
Krishna Garikipati


01.08ct. 1. Intro to C++ (Running Your Code, Basic Structure, Number Types, Vectors) (21:09) 
Gregory Teichert


01.08ct. 2. Intro to C++ (Conditional Statements, "for" Loops, Scope) (19:27) 
Gregory Teichert


01.08ct. 3. Intro to C++ (Pointers, Iterators) (14:01) 
Gregory Teichert


02.01. The Galerkin, or finitedimensional weak form (23:14) 
Krishna Garikipati


02.01.Response to a question (7:28) 
Krishna Garikipati


02.02. Basic Hilbert spaces  I (15:51) 
Krishna Garikipati


02.03. Basic Hilbert spaces  II (9:28) 
Krishna Garikipati


02.04. The finite element method for the onedimensional, linear, elliptic partial differential equation (22:53) 
Krishna Garikipati


02.04.Response to a question (6:21) 
Krishna Garikipati


02.05. Basis functions  I (14:55) 
Krishna Garikipati


02.06. Basis functions  II (14:43) 
Krishna Garikipati


02.07. The biunit domain  I (11:43) 
Krishna Garikipati


02.08. The biunit domain  II (16:19) 
Krishna Garikipati


02.09. The finite dimensional weak form as a sum over element subdomains  I (16:08) 
Krishna Garikipati


02.10. The finite dimensional weak form as a sum over element subdomains  II (12:24) 
Krishna Garikipati


02.10ct. 1. Intro to C++ (Functions) (13:27) 
Gregory Teichert


02.10ct. 2. Intro to C++ (C++ Classes) (16:43) 
Gregory Teichert


03.01. The matrixvector weak form  I  I (16:26) 
Krishna Garikipati


03.02. The matrixvector weak form  I  II (17:44) 
Krishna Garikipati


03.03. The matrixvector weak form  II  I (15:37) 
Krishna Garikipati


03.04. The matrixvector weak form  II  II (13:50) 
Krishna Garikipati


03.05. The matrixvector weak form  III  I (22:31) 
Krishna Garikipati


03.06. The matrixvector weak form  III  II (13:22) 
Krishna Garikipati


03.06ct. 1. Dealii.org, Running Deal.II on a Virtual Machine with Oracle Virtualbox (12:59) 
Gregory Teichert


03.06ct. 2. Intro to AWS; Using AWS on Windows (24:43) 
Gregory Teichert


03.06ct. 2c. Correction (3:31) 
Gregory Teichert


03.06ct. 3. Using AWS on Linux and Mac OS (7:42) 
Gregory Teichert


03.07. The final finite element equations in matrixvector form  I (21:02) 
Krishna Garikipati


03.08. The final finite element equations in matrixvector form  II (18:23) 
Krishna Garikipati


03.08.Response to a question (4:35) 
Krishna Garikipati


03.08ct. Coding Assignment 1 (main1.cc, Overview of C++ Class in FEM1.h) (19:34) 
Gregory Teichert


04.01. The pure Dirichlet problem  I (18:14) 
Krishna Garikipati


04.02. The pure Dirichlet problem  II (17:41) 
Krishna Garikipati


04.03. Higher polynomial order basis functions  I (22:55) 
Krishna Garikipati


04.04. Higher polynomial order basis functions  I  II (16:38) 
Krishna Garikipati


04.05. Higher polynomial order basis functions  II  I (13:38) 
Krishna Garikipati


04.06. Higher polynomial order basis functions  III (23:23) 
Krishna Garikipati


04.06ct. Coding Assignment 1 (Functions: Class Constructor to "basis_gradient") (14:40) 
Gregory Teichert


04.07. The matrixvector equations for quadratic basis functions  I  I (21:19) 
Krishna Garikipati


04.08. The matrixvector equations for quadratic basis functions  I  II (11:53) 
Krishna Garikipati


04.09. The matrixvector equations for quadratic basis functions  II  I (19:09) 
Krishna Garikipati


04.10. The matrixvector equations for quadratic basis functions  II  II (24:08) 
Krishna Garikipati


04.11. Numerical integration  Gaussian quadrature (13:57) 
Krishna Garikipati


04.11ct. 1. Coding Assignment 1 (Functions: "generate_mesh" to "setup_system") (14:21) 
Gregory Teichert


04.11ct.2. Coding Assignment 1 (Functions: "assemble_system") (26:58) 
Gregory Teichert


05.01. Norms  I (18:22) 
Krishna Garikipati


05.01ct. 1. Coding Assignment 1 (Functions: "solve" to "I2norm_of_error") (10:57) 
Gregory Teichert


05.01ct. 2. Visualization Tools (7:17) 
Gregory Teichert


05.02. Norms  II (18:21) 
Krishna Garikipati


05.02. Response to a question (5:45) 
Krishna Garikipati


05.03. Consistency of the finite element method (24:27) 
Krishna Garikipati


05.04. The best approximation property (21:32) 
Krishna Garikipati


05.05. Response to a question (3:31) 
Krishna Garikipati


05.05. The Pythagorean Theorem (13:14) 
Krishna Garikipati


05.06. Sobolev estimates and convergence of the finite element method (23:50) 
Krishna Garikipati


05.07. Finite element error estimates (22:07) 
Krishna Garikipati


06.01. Functionals. Free energy  I (17:38) 
Krishna Garikipati


06.02. Functionals. Free energy  II (13:20) 
Krishna Garikipati


06.03. Extremization of functionals (18:30) 
Krishna Garikipati


06.04. Derivation of the weak form using a variational principle (20:09) 
Krishna Garikipati


07.01. The strong form of steady state heat conduction and mass diffusion  I (18:24) 
Krishna Garikipati


07.02. Response to a question (1:27) 
Krishna Garikipati


07.02. The strong form of steady state heat conduction and mass diffusion  II (19:00) 
Krishna Garikipati


07.03. The strong form, continued (19:27) 
Krishna Garikipati


07.04. The weak form (24:33) 
Krishna Garikipati


07.05. The finitedimensional weak form  I (12:35) 
Krishna Garikipati


07.06. The finitedimensional weak form  II (15:56) 
Krishna Garikipati


07.07. Threedimensional hexahedral finite elements (21:30) 
Krishna Garikipati


07.08. Aside: Insight to the basis functions by considering the twodimensional case (16:43) 
Krishna Garikipati


07.09. Field derivatives. The Jacobian  I (12:38) 
Krishna Garikipati


07.10. Field derivatives. The Jacobian  II (14:20) 
Krishna Garikipati


07.11. The integrals in terms of degrees of freedom (16:25) 
Krishna Garikipati


07.12. The integrals in terms of degrees of freedom  continued (20:55) 
Krishna Garikipati


07.13. The matrixvector weak form  I (17:19) 
Krishna Garikipati


07.14. The matrixvector weak form II (11:20) 
Krishna Garikipati


07.15.The matrixvector weak form, continued  I (17:21) 
Krishna Garikipati


07.16. The matrixvector weak form, continued  II (16:08) 
Krishna Garikipati


07.17. The matrix vector weak form, continued further  I (17:40) 
Krishna Garikipati


07.18. The matrixvector weak form, continued further  II (17:18) 
Krishna Garikipati


08.01. Lagrange basis functions in 1 through 3 dimensions  I (18:58) 
Krishna Garikipati


08.02. Lagrange basis functions in 1 through 3 dimensions  II (12:36) 
Krishna Garikipati


08.02ct. Coding Assignment 2 (2D Problem)  I 
Gregory Teichert


08.03. Quadrature rules in 1 through 3 dimensions (17:03) 
Krishna Garikipati


08.03ct. 1. Coding Assignment 2 (2D Problem)  II (13:50) 
Gregory Teichert


08.03ct. 2. Coding Assignment 2 (3D Problem) 
Gregory Teichert


08.04. Triangular and tetrahedral elements  Linears  I (10:25) 
Krishna Garikipati


08.05. Triangular and tetrahedral elements  Linears  II (16:29) 
Krishna Garikipati


09.01. The finitedimensional weak form and basis functions  I (20:39) 
Krishna Garikipati


09.02. The finitedimensional weak form and basis functions  II (19:12) 
Krishna Garikipati


09.03. The matrixvector weak form (19:06) 
Krishna Garikipati


09.04. The matrixvector weak form  II (9:42) 
Krishna Garikipati


10.01. The strong form of linearized elasticity in three dimensions  I (09:58) 
Krishna Garikipati


10.02. The strong form of linearized elasticity in three dimensions  II (15:44) 
Krishna Garikipati


10.03. The strong form, continued (23:54) 
Krishna Garikipati


10.04. The constitutive relations of linearized elasticity (21:09) 
Krishna Garikipati


10.05. Response to a question (07:55) 
Krishna Garikipati


10.05. The weak form  I (17:37) 
Krishna Garikipati


10.06. The weak form  II (20:23) 
Krishna Garikipati


10.07. The finitedimensional weak form  Basis functions  I (18:23) 
Krishna Garikipati


10.08. The finitedimensional weak form  Basis functions  II (10:00) 
Krishna Garikipati


10.09. Element integrals  I (20:45) 
Krishna Garikipati


10.10. Element integrals  II (6:45) 
Krishna Garikipati


10.11. The matrixvector weak form  I (19:00) 
Krishna Garikipati


10.12. The matrixvector weak form  II (12:11) 
Krishna Garikipati


10.13. Assembly of the global matrixvector equations  I (20:40) 
Krishna Garikipati


10.14. Assembly of the global matrixvector equations  II (9:16) 
Krishna Garikipati


10.14ct. 1. Coding Assignment 3  I (10:19) 
Gregory Teichert


10.14ct. 2. Coding Assignment 3  II (19:55) 
Gregory Teichert


10.15. Dirichlet boundary conditions  I (21:23) 
Krishna Garikipati


10.16. Dirichlet boundary conditions  II (13:59) 
Krishna Garikipati


11.01. The strong form (16:29) 
Krishna Garikipati


11.02. The weak form, and finitedimensional weak form  I (18:44) 
Krishna Garikipati


11.03. The weak form, and finitedimensional weak form  II (10:15) 
Krishna Garikipati


11.04. Basis functions, and the matrixvector weak form  I (19:52) 
Krishna Garikipati


11.05. Basis functions, and the matrixvector weak form  II (12:03) 
Krishna Garikipati


11.05. Response to a question (00:51) 
Krishna Garikipati


11.06. Dirichlet boundary conditions; the final matrixvector equations (16:57) 
Krishna Garikipati


11.07. Time discretization; the Euler family  I (22:37) 
Krishna Garikipati


11.08. Time discretization; the Euler family  II (9:55) 
Krishna Garikipati


11.09. The vform and dform (20:54) 
Krishna Garikipati


11.09ct. 1. Coding Assignment 4  I (11:10) 
Gregory Teichert


11.09ct. 2. Coding Assignment 4  II (13:53) 
Gregory Teichert


11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition  I (17:24) 
Krishna Garikipati


11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition  II (12:55) 
Krishna Garikipati


11.12. Modal decomposition and modal equations  I (16:00) 
Krishna Garikipati


11.13. Modal decomposition and modal equations  II (16:01) 
Krishna Garikipati


11.14. Modal equations and stability of the timeexact single degree of freedom systems  I (10:49) 
Krishna Garikipati


11.15. Modal equations and stability of the timeexact single degree of freedom systems  II (17:38) 
Krishna Garikipati


11.16. Stability of the timediscrete single degree of freedom systems (23:25) 
Krishna Garikipati


11.17. Behavior of higherorder modes; consistency  I (18:57) 
Krishna Garikipati


11.18. Behavior of higherorder modes; consistency  II (19:51) 
Krishna Garikipati


11.19. Convergence  I (20:49) 
Krishna Garikipati


11.20. Convergence  II (16:38) 
Krishna Garikipati


12.01. The strong and weak forms (16:37) 
Krishna Garikipati


12.02. The finitedimensional and matrixvector weak forms  I (10:37) 
Krishna Garikipati


12.03. The finitedimensional and matrixvector weak forms  II (16:00) 
Krishna Garikipati


12.04. The timediscretized equations (23:15) 
Krishna Garikipati


12.05. Stability  I (12:57) 
Krishna Garikipati


12.06. Stability  II (14:35) 
Krishna Garikipati


12.07. Behavior of higherorder modes (19:32) 
Krishna Garikipati


12.08. Convergence (20:54) 
Krishna Garikipati

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01.01. Introduction. Linear elliptic partial differential equations  I (14:46) 
Krishna Garikipati


01.02. Introduction. Linear elliptic partial differential equations  II (13:01) 
Krishna Garikipati


01.03. Boundary conditions (22:18) 
Krishna Garikipati


01.04. Constitutive relations (20:06) 
Krishna Garikipati


01.05. Strong form of the partial differential equation. Analytic solution (22:44) 
Krishna Garikipati


01.06. Weak form of the partial differential equation  I (12:29) 
Krishna Garikipati


01.07. Weak form of the partial differential equation  II (15:05) 
Krishna Garikipati


01.08. Equivalence between the strong and weak forms  1 (25:10) 
Krishna Garikipati


01.08ct. 1. Intro to C++ (Running Your Code, Basic Structure, Number Types, Vectors) (21:09) 
Gregory Teichert


01.08ct. 2. Intro to C++ (Conditional Statements, "for" Loops, Scope) (19:27) 
Gregory Teichert


01.08ct. 3. Intro to C++ (Pointers, Iterators) (14:01) 
Gregory Teichert

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02.01. The Galerkin, or finitedimensional weak form (23:14) 
Krishna Garikipati


02.01.Response to a question (7:28) 
Krishna Garikipati


02.02. Basic Hilbert spaces  I (15:51) 
Krishna Garikipati


02.03. Basic Hilbert spaces  II (9:28) 
Krishna Garikipati


02.04. The finite element method for the onedimensional, linear, elliptic partial differential equation (22:53) 
Krishna Garikipati


02.04.Response to a question (6:21) 
Krishna Garikipati


02.05. Basis functions  I (14:55) 
Krishna Garikipati


02.06. Basis functions  II (14:43) 
Krishna Garikipati


02.07. The biunit domain  I (11:43) 
Krishna Garikipati


02.08. The biunit domain  II (16:19) 
Krishna Garikipati


02.09. The finite dimensional weak form as a sum over element subdomains  I (16:08) 
Krishna Garikipati


02.10. The finite dimensional weak form as a sum over element subdomains  II (12:24) 
Krishna Garikipati


02.10ct. 1. Intro to C++ (Functions) (13:27) 
Gregory Teichert


02.10ct. 2. Intro to C++ (C++ Classes) (16:43) 
Gregory Teichert

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03.01. The matrixvector weak form  I  I (16:26) 
Krishna Garikipati


03.02. The matrixvector weak form  I  II (17:44) 
Krishna Garikipati


03.03. The matrixvector weak form  II  I (15:37) 
Krishna Garikipati


03.04. The matrixvector weak form  II  II (13:50) 
Krishna Garikipati


03.05. The matrixvector weak form  III  I (22:31) 
Krishna Garikipati


03.06. The matrixvector weak form  III  II (13:22) 
Krishna Garikipati


03.06ct. 1. Dealii.org, Running Deal.II on a Virtual Machine with Oracle Virtualbox (12:59) 
Gregory Teichert


03.06ct. 2. Intro to AWS; Using AWS on Windows (24:43) 
Gregory Teichert


03.06ct. 2c. Correction (3:31) 
Gregory Teichert


03.06ct. 3. Using AWS on Linux and Mac OS (7:42) 
Gregory Teichert


03.07. The final finite element equations in matrixvector form  I (21:02) 
Krishna Garikipati


03.08. The final finite element equations in matrixvector form  II (18:23) 
Krishna Garikipati


03.08.Response to a question (4:35) 
Krishna Garikipati


03.08ct. Coding Assignment 01 
Krishna Garikipati


03.08ct. Coding Assignment 01 Template 
Krishna Garikipati


03.08ct. Coding Assignment 1 (main1.cc, Overview of C++ Class in FEM1.h) (19:34) 
Gregory Teichert

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04.01. The pure Dirichlet problem  I (18:14) 
Krishna Garikipati


04.02. The pure Dirichlet problem  II (17:41) 
Krishna Garikipati


04.03. Higher polynomial order basis functions  I (22:55) 
Krishna Garikipati


04.04. Higher polynomial order basis functions  I  II (16:38) 
Krishna Garikipati


04.05. Higher polynomial order basis functions  II  I (13:38) 
Krishna Garikipati


04.06. Higher polynomial order basis functions  III (23:23) 
Krishna Garikipati


04.06ct. Coding Assignment 1 (Functions: Class Constructor to "basis_gradient") (14:40) 
Gregory Teichert


04.07. The matrixvector equations for quadratic basis functions  I  I (21:19) 
Krishna Garikipati


04.08. The matrixvector equations for quadratic basis functions  I  II (11:53) 
Krishna Garikipati


04.09. The matrixvector equations for quadratic basis functions  II  I (19:09) 
Krishna Garikipati


04.10. The matrixvector equations for quadratic basis functions  II  II (24:08) 
Krishna Garikipati


04.11. Numerical integration  Gaussian quadrature (13:57) 
Krishna Garikipati


04.11ct. 1. Coding Assignment 1 (Functions: "generate_mesh" to "setup_system") (14:21) 
Gregory Teichert


04.11ct.2. Coding Assignment 1 (Functions: "assemble_system") (26:58) 
Gregory Teichert

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05.01. Norms  I (18:22) 
Krishna Garikipati


05.01ct. 1. Coding Assignment 1 (Functions: "solve" to "I2norm_of_error") (10:57) 
Gregory Teichert


05.01ct. 2. Visualization Tools (7:17) 
Gregory Teichert


05.02. Norms  II (18:21) 
Krishna Garikipati


05.02. Response to a question (5:45) 
Krishna Garikipati


05.03. Consistency of the finite element method (24:27) 
Krishna Garikipati


05.04. The best approximation property (21:32) 
Krishna Garikipati


05.05. Response to a question (3:31) 
Krishna Garikipati


05.05. The Pythagorean Theorem (13:14) 
Krishna Garikipati


05.06. Sobolev estimates and convergence of the finite element method (23:50) 
Krishna Garikipati


05.07. Finite element error estimates (22:07) 
Krishna Garikipati

Document Title  Creator  Downloads  License 

06.01. Functionals. Free energy  I (17:38) 
Krishna Garikipati


06.02. Functionals. Free energy  II (13:20) 
Krishna Garikipati


06.03. Extremization of functionals (18:30) 
Krishna Garikipati


06.04. Derivation of the weak form using a variational principle (20:09) 
Krishna Garikipati

Document Title  Creator  Downloads  License 

07.01. The strong form of steady state heat conduction and mass diffusion  I (18:24) 
Krishna Garikipati


07.02. Response to a question (1:27) 
Krishna Garikipati


07.02. The strong form of steady state heat conduction and mass diffusion  II (19:00) 
Krishna Garikipati


07.03. The strong form, continued (19:27) 
Krishna Garikipati


07.04. The weak form (24:33) 
Krishna Garikipati


07.05. The finitedimensional weak form  I (12:35) 
Krishna Garikipati


07.06. The finitedimensional weak form  II (15:56) 
Krishna Garikipati


07.07. Threedimensional hexahedral finite elements (21:30) 
Krishna Garikipati


07.08. Aside: Insight to the basis functions by considering the twodimensional case (16:43) 
Krishna Garikipati


07.09. Field derivatives. The Jacobian  I (12:38) 
Krishna Garikipati


07.10. Field derivatives. The Jacobian  II (14:20) 
Krishna Garikipati


07.11. The integrals in terms of degrees of freedom (16:25) 
Krishna Garikipati


07.12. The integrals in terms of degrees of freedom  continued (20:55) 
Krishna Garikipati


07.13. The matrixvector weak form  I (17:19) 
Krishna Garikipati


07.14. The matrixvector weak form II (11:20) 
Krishna Garikipati


07.15.The matrixvector weak form, continued  I (17:21) 
Krishna Garikipati


07.16. The matrixvector weak form, continued  II (16:08) 
Krishna Garikipati


07.17. The matrix vector weak form, continued further  I (17:40) 
Krishna Garikipati


07.18. The matrixvector weak form, continued further  II (17:18) 
Krishna Garikipati

Document Title  Creator  Downloads  License 

08.01. Lagrange basis functions in 1 through 3 dimensions  I (18:58) 
Krishna Garikipati


08.02. Lagrange basis functions in 1 through 3 dimensions  II (12:36) 
Krishna Garikipati


08.02ct. Coding Assignment 02 
Krishna Garikipati


08.02ct. Coding Assignment 02 Template 
Krishna Garikipati


08.02ct. Coding Assignment 2 (2D Problem)  I 
Gregory Teichert


08.03. Quadrature rules in 1 through 3 dimensions (17:03) 
Krishna Garikipati


08.03ct. 1. Coding Assignment 2 (2D Problem)  II (13:50) 
Gregory Teichert


08.03ct. 2. Coding Assignment 2 (3D Problem) 
Gregory Teichert


08.04. Triangular and tetrahedral elements  Linears  I (10:25) 
Krishna Garikipati


08.05. Triangular and tetrahedral elements  Linears  II (16:29) 
Krishna Garikipati

Document Title  Creator  Downloads  License 

09.01. The finitedimensional weak form and basis functions  I (20:39) 
Krishna Garikipati


09.02. The finitedimensional weak form and basis functions  II (19:12) 
Krishna Garikipati


09.03. The matrixvector weak form (19:06) 
Krishna Garikipati


09.04. The matrixvector weak form  II (9:42) 
Krishna Garikipati

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10.01. The strong form of linearized elasticity in three dimensions  I (09:58) 
Krishna Garikipati


10.02. The strong form of linearized elasticity in three dimensions  II (15:44) 
Krishna Garikipati


10.03. The strong form, continued (23:54) 
Krishna Garikipati


10.04. The constitutive relations of linearized elasticity (21:09) 
Krishna Garikipati


10.05. Response to a question (07:55) 
Krishna Garikipati


10.05. The weak form  I (17:37) 
Krishna Garikipati


10.06. The weak form  II (20:23) 
Krishna Garikipati


10.07. The finitedimensional weak form  Basis functions  I (18:23) 
Krishna Garikipati


10.08. The finitedimensional weak form  Basis functions  II (10:00) 
Krishna Garikipati


10.09. Element integrals  I (20:45) 
Krishna Garikipati


10.10. Element integrals  II (6:45) 
Krishna Garikipati


10.11. The matrixvector weak form  I (19:00) 
Krishna Garikipati


10.12. The matrixvector weak form  II (12:11) 
Krishna Garikipati


10.13. Assembly of the global matrixvector equations  I (20:40) 
Krishna Garikipati


10.14. Assembly of the global matrixvector equations  II (9:16) 
Krishna Garikipati


10.14ct. 1. Coding Assignment 03 
Krishna Garikipati


10.14ct. 1. Coding Assignment 03 Template 
Krishna Garikipati


10.14ct. 1. Coding Assignment 3  I (10:19) 
Gregory Teichert


10.14ct. 2. Coding Assignment 3  II (19:55) 
Gregory Teichert


10.15. Dirichlet boundary conditions  I (21:23) 
Krishna Garikipati


10.16. Dirichlet boundary conditions  II (13:59) 
Krishna Garikipati

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11.01. The strong form (16:29) 
Krishna Garikipati


11.02. The weak form, and finitedimensional weak form  I (18:44) 
Krishna Garikipati


11.03. The weak form, and finitedimensional weak form  II (10:15) 
Krishna Garikipati


11.04. Basis functions, and the matrixvector weak form  I (19:52) 
Krishna Garikipati


11.05. Basis functions, and the matrixvector weak form  II (12:03) 
Krishna Garikipati


11.05. Response to a question (00:51) 
Krishna Garikipati


11.06. Dirichlet boundary conditions; the final matrixvector equations (16:57) 
Krishna Garikipati


11.07. Time discretization; the Euler family  I (22:37) 
Krishna Garikipati


11.08. Time discretization; the Euler family  II (9:55) 
Krishna Garikipati


11.09. The vform and dform (20:54) 
Krishna Garikipati


11.09ct. 1. Coding Assignment 04 
Krishna Garikipati


11.09ct. 1. Coding Assignment 04 Template 
Krishna Garikipati


11.09ct. 1. Coding Assignment 4  I (11:10) 
Gregory Teichert


11.09ct. 2. Coding Assignment 4  II (13:53) 
Gregory Teichert


11.10. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition  I (17:24) 
Krishna Garikipati


11.11. Analysis of the integration algorithms for first order, parabolic equations; modal decomposition  II (12:55) 
Krishna Garikipati


11.12. Modal decomposition and modal equations  I (16:00) 
Krishna Garikipati


11.13. Modal decomposition and modal equations  II (16:01) 
Krishna Garikipati


11.14. Modal equations and stability of the timeexact single degree of freedom systems  I (10:49) 
Krishna Garikipati


11.15. Modal equations and stability of the timeexact single degree of freedom systems  II (17:38) 
Krishna Garikipati


11.16. Stability of the timediscrete single degree of freedom systems (23:25) 
Krishna Garikipati


11.17. Behavior of higherorder modes; consistency  I (18:57) 
Krishna Garikipati


11.18. Behavior of higherorder modes; consistency  II (19:51) 
Krishna Garikipati


11.19. Convergence  I (20:49) 
Krishna Garikipati


11.20. Convergence  II (16:38) 
Krishna Garikipati

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12.01. The strong and weak forms (16:37) 
Krishna Garikipati


12.02. The finitedimensional and matrixvector weak forms  I (10:37) 
Krishna Garikipati


12.03. The finitedimensional and matrixvector weak forms  II (16:00) 
Krishna Garikipati


12.04. The timediscretized equations (23:15) 
Krishna Garikipati


12.05. Stability  I (12:57) 
Krishna Garikipati


12.06. Stability  II (14:35) 
Krishna Garikipati


12.07. Behavior of higherorder modes (19:32) 
Krishna Garikipati


12.08. Convergence (20:54) 
Krishna Garikipati
