Differentiability properties of solutions of the equation -ε2δ u + ru=f(x,y) in a square
SIAM Journal on Mathematical Analysis
Finite volume methods for convection-diffusion problems
Modelling 94 Proceedings of the 1994 international symposium on Mathematical modelling and computational methods
Uniform Convergence of Finite-Difference Schemes for Reaction-Diffusion Interface Problems
Large-Scale Scientific Computing
Numerical treatment of fourth order singularly perturbed boundary value problems
NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications
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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 ε2. We construct finite volume difference schemes on condensed Shihskin meshes and prove ε-uniform convergence in discrete energy and maximum norms. Numerical experiments that agree with the theoretical results are given.