UP主： 封面： 简介：物理问题的有限元方法 Krishna Garikipati教授 密西根大学网课The Finite Element Method for Problems in Physics-University of Michigan
视频选集 01.01. Introduction. Linear elliptic partial differential equations - I 01.02. Introduction. Linear elliptic partial differential equations - II 01.03. Boundary conditions 01.04. Constitutive relations 01.05. Strong form of the partial differential equation. Analytic solution 01.06. Weak form of the partial differential equation - I 01.07. Weak form of the partial differential equation - II 01.08. Equivalence between the strong and weak forms 02.01. The Galerkin, or finite-dimensional weak form 02.02. Basic Hilbert spaces - I 02.03. Basic Hilbert spaces - II 02.04. The finite element method for the one-dimensional, linear, elliptic parti 02.05. Basis functions - I 02.06. Basis functions - II 02.07. The bi-unit domain - I 02.08. The bi-unit domain - II 02.09. The finite dimensional weak form as a sum over element subdomains - I 02.10. The finite dimensional weak form as a sum over element subdomains - II 03.01. The matrix-vector weak form - I - I 03.02. The matrix-vector weak form - I - II 03.03. The matrix-vector weak form - II - I 03.04. The matrix-vector weak form - II - II 03.05. The matrix-vector weak form - III - I 03.06. The matrix-vector weak form - III - II 03.07. The final finite element equations in matrix-vector form - I 03.08. The final finite element equations in matrix-vector form - II 04.01. The pure Dirichlet problem - I 04.02. The pure Dirichlet problem - II 04.02c. In-Video Correction 04.03. Higher polynomial order basis functions - I 04.03c0. In-Video Correction 04.03c1. In-Video Correction 04.04. Higher polynomial order basis functions - I - II 04.05. Higher polynomial order basis functions - II - I 04.06. Higher polynomial order basis functions - III 04.07. The matrix-vector equations for quadratic basis functions - I - I 04.08. The matrix-vector equations for quadratic basis functions - I - II 04.09. The matrix-vector equations for quadratic basis functions - II - I 04.10. The matrix-vector equations for quadratic basis functions - II - II 04.11. Numerical integration -- Gaussian quadrature 05.01. Norms - I 05.01c. In-Video Correction 05.02. Norms - II 05.03. Consistency of the finite element method 05.04. The best approximation property 05.05. The Pythagorean Theorem 05.06. Sobolev estimates and convergence of the finite element method 05.07. Finite element error estimates 06.01. Functionals. Free energy - I 06.02. Functionals. Free energy - II 06.03. Extremization of functionals 06.04. Derivation of the weak form using a variational principle 07.01. The strong form of steady state heat conduction and mass diffusion - I 07.02. The strong form of steady state heat conduction and mass diffusion - II 07.03. The strong form, continued 07.03c. In-Video Correction 07.04. The weak form 07.05. The finite-dimensional weak form - I 07.06. The finite-dimensional weak form - II 07.07. Three-dimensional hexahedral finite elements 07.08. Aside Insight to the basis functions by considering the two dimensional c 07.08c In-Video Correction 07.09. Field derivatives. The Jacobian - I 07.10. Field derivatives. The Jacobian - II 07.11. The integrals in terms of degrees of freedom 07.12. The integrals in terms of degrees of freedom - continued 07.13. The matrix-vector weak form - I 07.14. The matrix-vector weak form II 07.15.The matrix-vector weak form, continued - I 07.15c. In-Video Correction 07.16. The matrix-vector weak form, continued - II 07.17. The matrix vector weak form, continued further - I 07.17c. In-Video Correction 07.18. The matrix-vector weak form, continued further - II 07.18c. In-Video Correction 08.01. Lagrange basis functions in 1 through 3 dimensions - I 08.01c. In-Video Correction 08.02. Lagrange basis functions in 1 through 3 dimensions - II 08.03. Quadrature rules in 1 through 3 dimensions 08.04. Triangular and tetrahedral elements - Linears - I 08.05. Triangular and tetrahedral elements - Linears - II 09.01. The finite-dimensional weak form and basis functions - I 09.02. The finite-dimensional weak form and basis functions - II 09.03. The matrix-vector weak form 09.03c. In-Video Correction 09.04. The matrix-vector weak form - II 09.04c. In-Video Correction 10.01. The strong form of linearized elasticity in three dimensions - I 10.02. The strong form of linearized elasticity in three dimensions - II 10.02c. In-Video Correction 10.03. The strong form, continued 10.04. The constitutive relations of linearized elasticity 10.05. The weak form - I 10.06. The weak form - II 10.07. The finite-dimensional weak form - Basis functions - I 10.08. The finite-dimensional weak form - Basis functions - II 10.09. Element integrals - I 10.09c. In-Video Correction 10.10. Element integrals - II 10.11. The matrix-vector weak form - I 10.12. The matrix-vector weak form - II 10.13. Assembly of the global matrix-vector equations - I 10.14. Assembly of the global matrix-vector equations - II 10.14c. In Video Correction 10.15. Dirichlet boundary conditions - I 10.16. Dirichlet boundary conditions - II 11.01. The strong form 11.01c In-Video Correction 11.02. The weak form, and finite-dimensional weak form - I 11.03. The weak form, and finite-dimensional weak form - II 11.04. Basis functions, and the matrix-vector weak form - I 11.04c In-Video Correction 11.05. Basis functions, and the matrix-vector weak form - II 11.06. Dirichlet boundary conditions; the final matrix-vector equations 11.07. Time discretization; the Euler family - I 11.08. Time discretization; the Euler family - II 11.09. The v-form and d-form 11.10. Analysis of the integration algorithms for first order, parabolic equatio 11.11. Analysis of the integration algorithms for first order, parabolic equatio 11.11c. In-Video Correction 11.12. Modal decomposition and modal equations - I 11.13. Modal decomposition and modal equations - II 11.14. Modal equations and stability of the time-exact single degree of freedom 11.15. Modal equations and stability of the time-exact single degree of freedom 11.16. Stability of the time-discrete single degree of freedom systems 11.17. Behavior of higher-order modes; consistency - I 11.18. Behavior of higher-order modes; consistency - II 11.19. Convergence - I 11.20. Convergence - II 12.01. The strong and weak forms 12.02. The finite-dimensional and matrix-vector weak forms - I 12.03. The finite-dimensional and matrix-vector weak forms - II 12.04. The time-discretized equations 12.05. Stability - I 12.06. Stability - II 12.07. Behavior of higher-order modes 12.08. Convergence 12.08c. In-Video Correction Conclusion, and the Road Ahead