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Discontinuous Galerkin method
Discontinuous Galerkin method, archive since academic year 2019/20
Academic year 2024/25
Lecture Notes
LectureNotes_DGM.pdf
Week 1, February 17, 2025
- 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
- abstract error analysis, Section 1.2
Week 2, February 25, 2025
- basic notation, Section 1.3
- broken Sobolev spaces, Section 1.3
- mesh assumptions, Section 1.3
- discretization of the Laplace problem by DGM, Section 1.4
Week 3, March 3, 2025
- discretization of the Laplace problem by DGM, Section 1.4
- formulation of DG solution, Section 1.4
- multiplicative trace inequality, Section 1.5
- inverse inequality, Section 1.5
- approximation properties, Section 1.5
Week 4, March 10, 2025
- boundedness of the bilinear forms, Section 1.6
Week 5, March 17, 2025
- 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 6, March 24, 2025
- 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
Week 7, March 31, 2025
- finite volume method for the discretization of convective terms
pres2.pdf (contains an internal animation working only in acroread)
An additional external animation FV-FE.avi
Week 8, April 7, 2025
- Discontinuous Galerkin method for first order hyperbolic problems
pres3.pdf,
more detailed description is given in Chapter 6 in the Lecture notes
(not necessary to study!)
- stabilizaton -- capturing of discontinuities, Section 6.5
- approximation of non-polygonal boundaries, Section 6.6
Week 9, April 14, 2025
- DGM for the nonlinear convection-diffusion equation: Sections 2.1 – 2.2, in the Lecture notes.
Week 10, April 11, 2025
No lecture Easter
Week 11, April 28, 2025
- DGM for the nonlinear convection-diffusion equation: Sections 2.3 – 2.4 in the Lecture notes (skip Section 2.3.2)
Week 12, May 5, 2025
- DGM for the nonlinear convection-diffusion equation: Sections 2.4, 2.5, 2.7 in the Lecture notes
- Discontinuous Galerkin method for a convection-diffusion equation: summary of results
pres4.pdf
- test_DGM2.pdf – test (quiz) #2
- BDF DGM method: Chapter 3 in the Lecture notes, numerical experiments,
presentation: pres5.pdf