Finite Element Methods for Interface Problems: Robust Residual-Based A Posteriori Error Estimates
Provides theoretically guaranteed error bounds for interface problems, which is important for adaptive mesh refinement in computational mechanics and materials science.
This paper establishes robust residual-based a posteriori error estimates for finite element methods solving elliptic interface problems, with reliability bounds independent of the diffusion coefficient jump and no assumptions on its distribution.
For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the Crouzeix-Raviart nonconforming and the discontinuous Galerkin elements in both two- and three-dimensions, the global reliability bounds are established with constants independent of the jump of the diffusion coefficient. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.