Robust local problem error estimation for a singularly perturbed problem on anisotropic finite element meshes

Robust Local Problem Error Estimation for a Singularly Perturbed Problem on Anisotropic Finite Element Meshes

Singularly perturbed problems often yield solutions with strong directional features, e.g. with boundary layers. Such anisotropic solutions lend themselves to adapted, anisotropic discretizations. The quality of the corresponding numerical solution is a key issue in any computational simulation. To this end we present a new robust error estimator for a singularly perturbed reaction–diffusion pr...

Robust a Posteriori Error Estimation for a Singularly Perturbed Reaction-Diffusion Equation on Anisotropic Tetrahedral Meshes

Finite element methods for a singularly perturbed transmission problem

We consider a one-dimensional singularly perturbed transmission problem with two different diffusion coefficients. The solution will contain boundary layers only in the part of the domain where the diffusion coefficient is high. We derive and analyze various finite element approaches for the approximation of the solution and conduct numerical computations that show the robustness (or lack there...

An a posteriori error estimate for finite element approximations of a singularly perturbed advection-diffusion problem

In this paper the author presents an a posteriori error estimator for approximations of the solution to an advectiondiffusion equation with a non-constant, vector-valued diffusion coefficient e in a conforming finite element space. Based on the complementary variational principle, we show that the error of an approximate solution in an associated energy norm is bounded by the sum of the weighte...

Uniform error estimates in the finite element method for a singularly perturbed reaction-diffusion problem

Consider the problem− 2∆u+u = f with homogeneous Neumann boundary condition in a bounded smooth domain in RN . The whole range 0 < ≤ 1 is treated. The Galerkin finite element method is used on a globally quasi-uniform mesh of size h; the mesh is fixed and independent of . A precise analysis of how the error at each point depends on h and is presented. As an application, first order error estima...