Local modification of meshes for adaptive and/or multigrid finite-element methods
Journal of Computational and Applied Mathematics
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
A posteriori error estimates for elliptic problems in two and three space dimensions
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods
SIAM Review
Local problems on stars: a posteriori error estimators, convergence, and performance
Mathematics of Computation
Duality-based adaptive refinement for elliptic pdes
Duality-based adaptive refinement for elliptic pdes
Hi-index | 0.00 |
In this article, we develop and analyze a hierarchical-type error estimator for a general class of second-order linear elliptic boundary value problems in bounded three-dimensional domains. This type of indicator automatically satisfies a global lower bound inequality, thereby giving efficiency, without regularity assumptions beyond those giving well-posedness of the continuous and discrete problems. The main focus of the paper is then to establish the reverse reliability result: a global upper bound on the error in terms of the error estimate (plus an oscillation term), again without additional regularity assumptions. The proof of this inequality depends on a clever choice of the space in which the error indicator lies and a moment-capturing quasi-interpolation result. We finish the article with a series of numerical experiments to illustrate the behavior predicted by the theoretical results.