Finite element approximation of reaction–diffusion problems using an exponentially graded mesh. (15th November 2018) - Constantinou, P.; Franz, S.; Ludwig, L.; Xenophontos, C.
Abstract: We present the analysis of an h version Finite Element Method for the approximation of the solution to singularly perturbed reaction–diffusion problems posed in smooth domains Ω ⊂ R 2 . The method uses piecewise polynomials of degree p in each variable, defined on an exponentially graded mesh, optimally constructed for the approximation of exponential layers. We establish robust, optimal convergence rates in a variety of norms and illustrate our theoretical findings through numerical computations.