Patches of Finite Elements for Singularly-Perturbed Diffusion Reaction Equations with Discontinuous Coefficients
C. de Falco (Dublin City University, Republic of Ireland), M. Culpo (Bergische Universität Wuppertal, Germany) and E. O'Riordan (Dublin City University, Republic of Ireland)
Singularly perturbed Diffusion Reaction equations with non-smooth coefficients exhibit thin boundary and interior layers. Layer resolving methods for such problems are based on either fitted difference operators or on fitted meshes. Among the latter class, methods based on Shishkin-type meshes are especially attractive because of their simplicity. However, their applicability to multidimensional problems is constrained by the difficulty of generating structured conforming meshes for general domain geometries.
We present a numerical method for solving Diffusion Reaction equations on two completely overlapping unstructured meshes which reduces the requirements on mesh generation software when strong local refinement is needed to capture features that appear on different scales. Applications arising in semiconductor device simulation and heat diffusion are presented.