Conference abstracts

Session B6 - Multiresolution and Adaptivity in Numerical PDEs

July 15, 15:00 ~ 15:25 - Room T1

Optimal convergence rates for adaptive FEM for compactly perturbed elliptic problems

Dirk Praetorius

TU Wien, Austria   -   dirk.praetorius@tuwien.ac.at

We consider adaptive FEM for problems, where the corresponding bilinear form is symmetric and elliptic up to some compact perturbation. We prove that adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a priori assumption that the underlying meshes are sufficiently fine. In particular, our analysis covers adaptive mesh-refinement for the Helmholtz equation from where our interest originated.

Joint work with Alex Bespalov (University of Birmingham, UK) and Alexander Haberl (TU Wien, Austria).

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