A two-grid method on layer-adapted meshes for a semilinear 2d reaction-diffusion problem

Authors:
Ivanka T. Angelova;Lubin G. Vulkov
Affiliations:
Faculty of Natural Science and Education, University of Rousse, Rousse, Bulgaria;Faculty of Natural Science and Education, University of Rousse, Rousse, Bulgaria
Venue:
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
Year:
2009

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Abstract

A singularly perturbed semilinear reaction-diffusion equation, posed in the unit square, is discetizied by a two-grid scheme on layer-adapted meshes In the first step, the nonlinear problem is discretized on coarse grid In the second step, the problem is discretized on a fine grid and linearized around the interpolation of the computed solution on the first step We show theoretically and numerically that the global error on Shishkin or Bakhvalov mesh is the same as would have been obtained if the nonlinear problem had been solved directly on the fine grid.