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.Comment: 26 pages, 6 figures. An earlier version of this paper appeared on
November 13, 2014 in
http://www.brown.edu/research/projects/scientific-computing/reports/201
