Abstract
A multigrid algorithm with adaptive semirefinement is presented for the solution of convection-diffusion problems. The method is based on the discontinuous Galerkin discretisation, which can conveniently handle grid adaptation. The algorithm is presented here for 2D problems, but it can be generalized for 3D. Rectangular finite elements are used and during the process of adaptation they may be refined in the x, y or in both (x and y) directions.
The adaptation criterion is based on the comparison of the discrete solution on the finest grid and its restrictions to the next (in the x and y directions) grids. It refines in the x or/and y direction those cells, where the corresponding difference is too large.
The numerical experiments show that the algorithm may be successfully used for resolution of boundary and interior layers. The comparison with a similar adaptive refinement multigrid algorithm shows that significantly less computer resources may be used for layers, almost parallel to the x or y axis.
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Vasileva, D. (2009). On an Adaptive Semirefinement Multigrid Algorithm for Convection-Diffusion Problems. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_67
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DOI: https://doi.org/10.1007/978-3-642-00464-3_67
Publisher Name: Springer, Berlin, Heidelberg
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