论文信息 - Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy

Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy

We consider a singularly perturbed reaction-diffusion elliptic problem in two dimensions (x,y), with strongly anisotropic coefficients and line interface. The second order derivative with respect to x is multiplied by a small parameter ɛ2. We construct finite volume difference schemes on condensed Shihskin meshes and prove ɛ-uniform convergence in discrete energy and maximum norms. Numerical experiments that agree with the theoretical results are given.

Lubin G. Vulkov | Iliya A. Brayanov

[1] A. A. Samarskii,et al. The Theory of Difference Schemes , 2001 .

[2] J. J. Miller,et al. Fitted Numerical Methods for Singular Perturbation Problems , 1996 .

[3] Jichun Li. Quasioptimal uniformly convergent finite element methods for the elliptic boundary layer problem , 1997 .

[4] Natalia Kopteva,et al. The two-dimensional sobolev inequality in the case of an arbitrary grid , 1998 .

[5] Torsten Linß,et al. Asymptotic Analysis and Shishkin-Type Decomposition for an Elliptic Convection–Diffusion Problem , 2001 .

[6] F. Brezzi,et al. Mathematical models and finite elements for reservoir simulation : single phase, multiphase and multicomponent flows through porous media , 1988 .

[7] G. Wittum,et al. On Robust and Adaptive Multi-Grid Methods , 1994 .

[8] R. B. Kellogg,et al. Differentiability properties of solutions of the equation -ε 2 δ u + ru = f ( x,y ) in a square , 1990 .

[9] Martin Stynes,et al. Finite volume methods for convection-diffusion problems , 1995, Irish Mathematical Society Bulletin.

[10] Lutz Tobiska,et al. Numerical Methods for Singularly Perturbed Differential Equations , 1996 .