Module "Advanced Computational Partial Differential Equation" (10-MAT-MM2CPDE)

Module "Advanced Computational Partial Differential Equations" (10-MAT-MM2CPDE, SS 2026)

Jun.-Prof. Dr. Mira Schedensack
Universität Leipzig
Fakultät für Mathematik und Informatik
Mathematisches Institut

Participants:

This lecture is suitable for students in mathematics (Bachelor, Master, Diploma) and in mathematical physics with the standard knowledge from the introductory lectures and functional analysis as well as from basic computational partial differential equations (standard Galerkin FEM).

Content:

The standard (or conforming) Galerkin finite element methods (FEMs) are based on a space V_h that is a subset of the space, where the continouos problem is posed. In many contexts, e.g., a divergence-free condition of the solution, smooth test functions, meshes with different shapes, or ansatz functions with variable polynomial degrees, those methods become complicated. To break with the conformity relation can lead to easier methods. However, this leads to additional consistency or nonconformity errors in the error analysis. The lecture will introduce several non-standard FEMs, in particular non-conforming and discontinuous Galerkin FEMs. The a priori and a posteriori error analysis of the methods, as well as their implementations and relations between different FEMs are discussed.

Time of lectures

The lecture will take place on Monday at 11:15-12:45 in P701 and Tuesday at 09:15-10:45 in A314. The corresponding seminar will take place on Tuesday at 11:15-12:45 in P701.

News

On 01. and 02. June, the lecture (and seminar) has to be cancelled.

On 19. May 2026, the evaluation of the lecture will take place.

The first lecture will take place on 07. April 2026.

Exam

To examination will consist of a presentation and its written elaboration in the seminar and an oral examination (for master or bachelor students), see also the Modulbeschreibungen.