Error estimates for linear finite elements on Bakhvalov-type meshes

Hans-Görg Roos

Displaying similar documents to “Error estimates for linear finite elements on Bakhvalov-type meshes”

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

Similarity:

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.

Some properties of the discontinuous Galerkin method for one-dimensional singularly perturbed problems.

Roos, Hans-Görg, Zarin, Helena (2003)

Novi Sad Journal of Mathematics

Similarity:

A numerical method for a singularly perturbed three-point boundary value problem.

Çakır, Musa, Amiraliyev, Gabil M. (2010)

Journal of Applied Mathematics

Similarity:

A robust computational technique for a system of singularly perturbed reaction-diffusion equations

Vinod Kumar, Rajesh Bawa, Arvind Lal (2014)

International Journal of Applied Mathematics and Computer Science

Similarity:

A robust computational technique for a system of singularly perturbed reaction-diffusion equations

Vinod Kumar, Rajesh Bawa, Arvind Lal (2014)

International Journal of Applied Mathematics and Computer Science

Similarity:

Opposing flows in a one dimensional convection-diffusion problem

Eugene O’Riordan (2012)

Open Mathematics

Similarity:

In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference...

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

Similarity:

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...