Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 35, Issue 2, Pages A861-A885Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120874606
Keywords
adaptive finite element algorithm; unstructured triangular anisotropic meshes; DWR method; linear and quadratic finite elements; patch-wise higher-order interpolation recovery
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Funding
- Ministerio de Ciencia e Innovacion of Spain [MTM2010-18079]
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We propose in this paper an anisotropic, adaptive, finite element algorithm for steady, linear advection-diffusion-reaction problems with strong anisotropic features. The error analysis is based on the dual weighted residual methodology, allowing us to perform goal-oriented adaptation of a certain functional J(u) of the solution and derive an optimal metric tensor for local mesh adaptation with linear and quadratic finite elements. As a novelty, and to evaluate the weights of the error estimator on unstructured meshes composed of anisotropic triangles, we make use of a patchwise, higher-order interpolation recovery readily extendable to finite elements of arbitrary order. We carry out a number of numerical experiments in two dimensions so as to prove the capabilities of the goal-oriented adaptive method. We compute the convergence rate and the effectivity index for a series of output functionals of the solution. The results show the good performance of the algorithm with linear as well as quadratic finite elements.
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