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.
Original language | English |
---|---|
Pages (from-to) | 318-340 |
Number of pages | 23 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 317 |
Early online date | 19 Dec 2016 |
DOIs | |
Publication status | Published - 15 Apr 2017 |
Keywords
- Adaptive mesh-refinement
- Optimal convergence rates
- a posteriori error estimate
- Helmholtz equation