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We present a locally adapted parametric finite element method for interfaceproblems. For this adapted finite element method we show optimal convergencefor elliptic interface problems with a discontinuous diffusion parameter. Themethod is based on the adaption of macro elements where a local basisrepresents the interface. The macro elements are independent of the interfaceand can be cut by the interface. A macro element which is a triangle in thetriangulation is divided into four subtriangles. On these subtriangles, thebasis functions of the macro element are interpreted as linear functions. Theposition of the vertices of these subtriangles is determined by the location ofthe interface in the case a macro element is cut by the interface. Quadratureis performed on the subtriangles via transformations to a reference element.Due to the locality of the method, its use is well suited on distributedarchitectures.

The locally adapted patch finite element method for interface problems on triangular meshes