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How accurate is the streamline-diffusion FEM inside characteristic (boundary and interior) layers? (English) Zbl 1112.76392

Summary: Two model two-dimensional singularly perturbed convection-diffusion problems are considered whose solutions may have characteristic boundary and interior layers. They are solved numerically by the streamline-diffusion finite element method using piecewise linear or bilinear elements. We investigate how accurate the computed solution is in characteristic-layer regions if anisotropic layer-adapted meshes are used. It is shown that the streamline-diffusion formulation may, in the maximum norm, imply only first-order accuracy in characteristic-layer regions. Numerical experiments are presented that support our theoretical predictions.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76R99 Diffusion and convection
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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References:

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