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Discontinuous Galerkin method
Discontinuous Galerkin method, archive since academic year 2019/20
Academic year 2023/24
Lecture Notes
LectureNotes_DGM.pdf
Week 1, February 20, 2024
- Motivation: numerical solution of partial differential equations,
presentation Lecture_DGM1.pdf (full),
Lecture_DGM1_brief.pdf (brief, suitable for printing)
- Propagation by a peak by connvection: conv.avi
- Propagation by a peak by diffusion: diff.avi
- Propagation by a peak by connvection-diffusion: conv+diff.avi
- Effect of diffusion for 1D linear convection-diffusion equation:
exactCD.avi
- Comparison of FEM and FVM for 1D linear convection:
FV-FE.avi
Week 2, February 21, 2024
- abstract error analysis, Section 1.2
- basic notation, Section 1.3
- broken Sobolev spaces, Section 1.3
Week 3, March 5, 2024
- mesh assumptions, Section 1.3
- discretization of the Laplace problem by DGM, Section 1.4
- formulation of DG solution, Section 1.4
Week 4, March 12, 2024
- multiplicative trace inequality, Section 1.5
- inverse inequality, Section 1.5
- approximation properties, Section 1.5
Week 5, March 19, 2024
- boundedness of the bilinear forms, Section 1.6
- coercivity, Section 1.6
Week 6, March 26, 2024
- coercivity, Section 1.6
- existence of the solution, Section 1.6
- abstract error estimate in the DG-norm, Section 1.7
- error estimate in terms of h , Section 1.7
Week 7, April 2, 2024
- error estimate in terms in the L^2-norm
- numerical experiments, experimental order of convergence
- pres1.pdf – summary of the main results of Chapter 1 from Lecture notes
- test_DGM1.pdf – test (quiz) #1