Abstract
In this paper we introduce a discontinuous finite element method. In our approach, it is possible to combine the advantages of finite element and finite difference methods. The main ingredients are numerical flux approximation and local orthogonal basis functions. The scheme is defined on arbitrary triangulations and two different error indicators are derived. Especially the second one is closely connected to our approach and able to handle arbitrary varying flow directions. Numerical resuls are given for boundary value problems in two dimensions. They demonstrate the performance of the scheme, combined with the two error indicators.
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