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

Opposing flows in a one dimensional convection-diffusion problem

Eugene O’Riordan (2012)

Open Mathematics

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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

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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 × N , N × N and N × N meshes. It is shown that the combination FEM yields (up to a factor ln N ) the same order of accuracy in...

A finite element method on composite grids based on Nitsche’s method

Anita Hansbo, Peter Hansbo, Mats G. Larson (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we propose a finite element method for the approximation of second order elliptic problems on composite grids. The method is based on continuous piecewise polynomial approximation on each grid and weak enforcement of the proper continuity at an artificial interface defined by edges (or faces) of one the grids. We prove optimal order a priori and energy type a posteriori error estimates in 2 and 3 space dimensions, and present some numerical examples.