2011/04/05 by Serge Nicaise, Nicaise, Serge, Xenophontos Christos +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1104.0766
arxiv created 2011/04/05 · arxiv updated 2011/04/06
We consider a two-dimensional singularly perturbed transmission problem with two different diffusion coefficients, in a domain with smooth (analytic) boundary. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high and interface layers along the interface. Utilizing existing and newly derived regularity results for the exact solution, we design a robust hp finite element method for its approximation. Under the assumption of analytic input data, we show that the method converges at an exponential rate, provided the mesh and polynomial degree distribution are chosen appropriately. Numerical results illustrating our theoretical findings are also included.