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• W2030076475 abstract "Convection-diffusion problems posed on the unit square and with solutions displaying exponential layers are solved using a sparse grid Galerkin finite element method with Shishkin meshes. Writing N for the maximum number of mesh intervals in each coordinate direction, our “combination” method simply adds or subtracts solutions that have been computed by the Galerkin FEM on $$ N times sqrt N , sqrt N times N $$ and $$ sqrt N times sqrt N $$ meshes. It is shown that the combination FEM yields (up to a factor ln N) the same order of accuracy in the associated energy norm as the Galerkin FEM on an N × N mesh, but it requires only $$ mathcal{O} $$ (N 3/2) degrees of freedom compared with the $$ mathcal{O} $$ (N 2) used by the Galerkin FEM. An analogous result is also proved for the streamline diffusion finite element method." @default.
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• W2030076475 date "2009-06-01" @default.
• W2030076475 modified "2023-10-17" @default.
• W2030076475 title "The combination technique for a two-dimensional convection-diffusion problem with exponential layers" @default.
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• W2030076475 doi "https://doi.org/10.1007/s10492-009-0013-9" @default.
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