We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to the right-hand side in the standard variational formulation of the problem. We prove optimal error estimates of the methods on general quasi-uniform and shape regular meshes in maximum norms. In addition, we apply the method to a Stokes interface problem, adding correction terms for the velocity and the pressure, obtaining optimal convergence results.
|Original language||English (US)|
|Number of pages||23|
|Journal||ESAIM: Mathematical Modelling and Numerical Analysis|
|State||Published - Sep 1 2016|
- Finite elements
- Interface problems
- Pointwise estimates