Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4964108 | Computer Methods in Applied Mechanics and Engineering | 2017 | 23 Pages |
Abstract
We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Gårding inequality, 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. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Alex Bespalov, Alexander Haberl, Dirk Praetorius,