Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.
Roos, Hans-Görg, Zarin, Helena (2003)
Novi Sad Journal of Mathematics
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Displaying similar documents to “The combination technique for a two-dimensional convection-diffusion problem with exponential layers”
Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.
Error estimates for linear finite elements on Bakhvalov-type meshes
Hans-Görg Roos (2006)
Applications of Mathematics
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For convection-diffusion problems with exponential layers, optimal error estimates for linear finite elements on Shishkin-type meshes are known. We present the first optimal convergence result in an energy norm for a Bakhvalov-type mesh.
Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D
Hans-Görg Roos, Martin Schopf (2012)
Applications of Mathematics
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So far optimal error estimates on Bakhvalov-type meshes are only known for finite difference and finite element methods solving linear convection-diffusion problems in the one-dimensional case. We prove (almost) optimal error estimates for problems with exponential boundary layers in two dimensions.
-widths for singularly perturbed problems
Martin Stynes, R. Bruce Kellogg (2002)
Mathematica Bohemica
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Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.