Exact integration formulas for the finite volume element method on simplicial meshes |
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| Authors: | TV Voitovich S Vandewalle |
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| Institution: | 1. Institute of Applied Mathematics, Albert‐Ludwigs‐Universit?t Freiburg, D‐79104 Freiburg, Germany;2. Department of Computer Science, Katholieke Universiteit Leuven, B‐3001 Leuven, BelgiumDepartment of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B‐3001 Leuven, Belgium |
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| Abstract: | This article considers the technological aspects of the finite volume element method for the numerical solution of partial differential equations on simplicial grids in two and three dimensions. We derive new classes of integration formulas for the exact integration of generic monomials of barycentric coordinates over different types of fundamental shapes corresponding to a barycentric dual mesh. These integration formulas constitute an essential component for the development of high‐order accurate finite volume element schemes. Numerical examples are presented that illustrate the validity of the technology. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 |
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| Keywords: | finite volume element method barycentric coordinates integration formulas |
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