Adaptive remeshing and \(h-p\) domain decomposition
An appropriate combination of mesh refinement (\(h\)-version) and increase of the shape functions' polynomial degree (\(p\)-version) yield, for linear elliptic boundary value problems, an exponential rate of convergence in the energy norm even if the exact solution is singular. The present paper presents a method which uses an \(h\)-\(p\)-approximation for a domain decomposition with fully overlapping domains, allowing \(C^ 0\)- continuous approximation for geometrically incompatible mesh refinement to be obtained [cf. \textit{J. H. Bramble, R. E. Ewing, R. R. Parashkevov} and \textit{J. E. Pasciak}, SIAM J. Sci. Stat. Comput. 13, No. 1, 397-410 (1992; Zbl 0746.65084)]. The method is applied to a reaction-diffusion problem resulting from semiconductor process simulation. By means of numerical examples it is illustrated that the foregoing approach is well suited for problems with sharp interior layers or shock-like behaviour.
scientific article; zbMATH DE number 429033
scientific article