Robust recovery-type a posteriori error estimators for streamline upwind/Petrov Galerkin discretizations for singularly perturbed problems

Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems

A procedure for the construction of robust, upper bounds for the error in the finite element approximation of singularly perturbed reaction diffusion problems was presented in [2] which entailed the solution of an infinite dimensional local boundary value problem. It is not possible to solve this problem exactly and this fact was recognised in the above work where it was indicated that the limi...

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

Numerical Study of Maximum Norm a Posteriori Error Estimates for Singularly Perturbed Parabolic Problems

A second-order singularly perturbed parabolic equation in one space dimension is considered. For this equation, we give computable a posteriori error estimates in the maximum norm for two semidiscretisations in time and a full discretisation using P1 FEM in space. Both the Backward-Euler method and the Crank-Nicolson method are considered, and certain critical details of the implementation are ...

Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems

Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polyhedral domains. Standard finite element approximations are considered. The error constants are independent of the diameters of mesh elements and the small perturbation parameter. In our analysis, we employ sharp bounds on the Green’s function of ...

Maximum-Norm A Posteriori Error Estimates for Singularly Perturbed Reaction-Diffusion Problems on Anisotropic Meshes

Lu :“ ́ε4u` fpx, y;uq “ 0 for px, yq P Ω, u “ 0 on BΩ, (1.1) posed in a, possibly non-Lipschitz, polygonal domain Ω Ă R. Here 0 ă ε ď 1. We also assume that f is continuous on ΩˆR and satisfies fp ̈; sq P L8pΩq for all s P R, and the one-sided Lipschitz condition fpx, y;uq ́ fpx, y; vq ě Cf ru ́ vs whenever u ě v, with some constant Cf ě 0. Then there is a unique solution u PW 2 ` pΩq ĎW 1 q Ă CpΩ̄q...