Abstract
Although adaptive finite element methods for solving elliptic problems often work well in practice, they are usually not proven to converge. For Poisson like problems, an exception is given by the method of Dörfler ([8]), that was later improved by Morin, Nochetto and Siebert ([11]). In this paper we extend these methods by constructing an adaptive finite element method for a singularly perturbed reaction-diffusion equation that, in energy norm, converges uniformly in the size of the reaction term. Moreover, in this algorithm the arising Galerkin systems are solved only inexactly, so that, generally, the number of arithmetic operations is equivalent to the number of triangles in the final partition.
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This work was supported by the Netherlands Organization for Scientific Research and by the EU-IHP project “Breaking Complexity.”
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Stevenson, R. The uniform saturation property for a singularly perturbed reaction-diffusion equation. Numer. Math. 101, 355–379 (2005). https://doi.org/10.1007/s00211-005-0606-5
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DOI: https://doi.org/10.1007/s00211-005-0606-5