Finite Element Methods for Interface Problems: Robust and Local Optimal A Priori Error Estimates
Provides theoretical guarantees for finite element methods in solving interface problems, which are important in computational science and engineering.
The paper establishes robust and locally optimal a priori error estimates for several finite element methods for elliptic interface problems, without assumptions on the diffusion coefficient distribution.
For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to local regularity of the solution. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.