Stopping Criterion for Adaptive Algorithm
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
The adaptive immersed interface finite element method for elliptic and Maxwell interface problems
Journal of Computational Physics
Convergence analysis of an adaptive edge element method for Maxwell's equations
Applied Numerical Mathematics
Advances in Computational Mathematics
Constraint-Free Adaptive FEMs on Quadrilateral Nonconforming Meshes
Journal of Scientific Computing
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The successful implementation of adaptive finite element methods based on a posteriori error estimates depends on several ingredients: an a posteriori error indicator, a refinement/coarsening strategy, and the choice of various parameters. The objective of the paper is to examine the influence of these factors on the performance of adaptive finite element methods for a model problem: the linear elliptic equation with strongly discontinuous coefficients. We derive a new a posteriori error estimator which depends locally on the oscillations of the coefficients around singular points. Extensive numerical experiments are reported to support our theoretical results and to show the competitive behaviors of the proposed adaptive algorithm.