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We present higher-order piecewise continuous finite element methods forsolving a class of interface problems in two dimensions. The method is based oncorrection terms added to the right-hand side in the standard variationalformulation of the problem. We prove optimal error estimates of the methods ongeneral quasi-uniform and shape regular meshes in maximum norms. In addition,we apply the method to a Stokes interface problem, adding correction terms forthe velocity and the pressure, obtaining optimal convergence results.

Higher-order finite element methods for elliptic problems with interfaces