Abstract A singularly perturbed reaction-diffusion problem is considered. The small diffusion coefficient generically leads to solutions
with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution
is reflected by using anisotropic meshes which can improve the accuracy of the discretization considerably. The main focus is on a posteriori error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect
to the small perturbation parameter. The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic
mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations).
Altogether, reliable and efficient a posteriori error estimation is achieved for the finite volume method on anisotropic meshes. Numerical experiments in 2D underline the
applicability of the theoretical results in adaptive computations.
with boundary layers. The problem is discretized by a vertex-centered finite volume method. The anisotropy of the solution
is reflected by using anisotropic meshes which can improve the accuracy of the discretization considerably. The main focus is on a posteriori error estimation. A residual type error estimator is proposed and rigorously analysed. It is shown to be robust with respect
to the small perturbation parameter. The estimator is also robust with respect to the mesh anisotropy as long as the anisotropic
mesh sufficiently reflects the anisotropy of the solution (which is almost always the case for sensible discretizations).
Altogether, reliable and efficient a posteriori error estimation is achieved for the finite volume method on anisotropic meshes. Numerical experiments in 2D underline the
applicability of the theoretical results in adaptive computations.
- Content Type Journal Article
- DOI 10.1007/s10915-010-9352-7
- Authors
- M. Afif, Université Cadi Ayyad Faculté des Sciences-Semlalia, Laboratoire LIBMA B.P. 2390 Marrakech Maroc
- B. Amaziane, Université de Pau et des Pays de l’Adour Laboratoire de Mathématiques et de leurs Applications, CNRS-UMR 5142 av. de l’Université 64000 Pau France
- G. Kunert, IAV GmbH 09120 Chemnitz Germany
- Z. Mghazli, Université Ibn Tofaïl Faculté des Sciences, Laboratoire LIRNE-Equipe EIMA B.P. 133 Kénitra Maroc
- S. Nicaise, Université Lille Nord de France, UVHC LAMAV, FR CNRS 2956 59313 Valenciennes Cedex 9 France
- Journal Journal of Scientific Computing
- Online ISSN 1573-7691
- Print ISSN 0885-7474
