Fully computable a posteriori error estimator using anisotropic flux equilibration on anisotropic meshes
For researchers in numerical analysis and computational PDEs, this provides a rigorous error estimator for anisotropic meshes, which is an incremental improvement over existing isotropic methods.
The paper develops fully computable a posteriori error estimates for singularly perturbed semilinear reaction-diffusion equations on anisotropic meshes, using anisotropic flux equilibration. The error constants are independent of mesh element diameters, aspect ratios, and the small perturbation parameter.
Fully computable a posteriori error estimates in the energy norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. To deal with the latter, we employ anisotropic quadrature and explicit anisotropic flux reconstruction. Prior to the flux equilibration, divergence-free corrections are introduced for pairs of anisotropic triangles sharing a short edge. We also give an upper bound for the resulting estimator, in which the error constants are independent of the diameters and the aspect ratios of mesh elements, and of the small perturbation parameter.