NEW: 101.A35, opens an external URL in a new window AKNUM: Iterative Solvers in Adaptive Finite Element Methods (VO 2,0) 2024W

The first meeting to decide the time/place of the lecture and provide informations will take place 

         on the 1st of October, at 12:00, in the seminar room DA 06 G14, opens an external URL in a new window 

To register please send me an e-mail (ani.miraci@asc.tuwien.ac.at)

Information:

• Semester hours: 2.0

• Credits: 3.0

• Type: VO Lecture

• Format: Presence

Learning outcomes: After successful completion of the course, students are able to...

• formulate an adaptive mesh-refinement algorithm employing an iterative solver for elliptic PDEs

• formulate an optimal complexity multilevel iterative solver

• explain the robustness of the solver contraction with respect to the discretization parameters

• how to derive a-posteriori error estimates for the algebraic and the discretization errors

• how to derive stopping criteria for the iterative solver

• state convergence and optimality of adaptive algorithms

Subject of the course:

• introduction to the adaptive finite element method (AFEM)

• introduction to multigrid methods (MG)

• stable decomposititons and strengthened Cauchy—Schwarz inequalities

• h- and p-robustness of the algebraic error contraction of multigrid

• a-posteriori-steering and adaptivity in algebraic solvers

• optimal convergence rates and optimal computational complexity of adaptive algorithms

Teaching methods: Presentation and proof of the mathematical results as well as of some numerical experiments

Mode of examination: Oral

The course is intended to be as self-contained as possible, nonetheless the following previous courses are recommended 

• 101.506 Numerics of partial differential equations: stationary problems 

• 101.888 AKNUM : A posteriori error estimation and adaptive FEM

Language: English