Article
Keywords:
numerical analysis; convection-diffusion problem; boundary layer; uniform convergence
Summary:
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.
References:
[1] A. S. Bakhvalov:
On the optimization of methods for solving boundary value problems with boundary layers. Zh. Vychisl. Mat. Mat. Fiz. 9 (1969), 841–859. (Russian)
MR 0255066
[3] M. Dobrowolski: Finite Elemente. University textbook of Würzburg, 1998.
[6] H.-G. Roos, M. Stynes, L. Tobiska:
Numerical Methods for Singularly Perturbed Differential Equations. Convection-Diffusion and Flow Problems. Springer-Verlag, Berlin, 1996.
MR 1477665
[7] W. W. Shaidurov, B. M. Bagaev, and E. D. Karepova:
Numerical Methods for Problems with Boundary Layers II. Nauka, Novosibirsk, 2002. (Russian)
MR 2029041
[8] M. Stynes, E. O’Riordan:
A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem. J. Math. Anal. Appl. 214 (1997), 36–54.
DOI 10.1006/jmaa.1997.5581 |
MR 1645503