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A new discontinuous finite volume method for elliptic problems. (English) Zbl 1079.65116

The author considers a new discontinuous finite volume method for second order linear elliptic boundary value problems. The method uses discontinuous piecewise polynomials in order to provide the trial function space. An optimal order error estimate is obtained in a discrete norm. The method seems to have important advantages such as a high order accuracy, parallelizability, localizability and the possibility to handle complex geometries.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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