Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D

Hans-Görg Roos; Martin Schopf

Displaying similar documents to “Analysis of finite element methods on Bakhvalov-type meshes for linear convection-diffusion problems in 2D”

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.

The combination technique for a two-dimensional convection-diffusion problem with exponential layers

Sebastian Franz, Fang Liu, Hans-Görg Roos, Martin Stynes, Aihui Zhou (2009)

Applications of Mathematics

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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...

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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A priori diffusion-uniform error estimates for singularly perturbed problems: Midpoint-DG discretization

Vlasák, Miloslav, Kučera, Václav

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We deal with a nonstationary semilinear singularly perturbed convection–diffusion problem. We discretize this problem by discontinuous Galerkin method in space and by midpoint rule in time. We present diffusion–uniform error estimates with sketches of proofs.