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Finite volumes and mixed Petrov-Galerkin finite elements: The unidimensional problem

✍ Scribed by François Dubois

Publisher
John Wiley and Sons
Year
2000
Tongue
English
Weight
446 KB
Volume
16
Category
Article
ISSN
0749-159X

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✦ Synopsis

For Laplace operator in one space dimension, we propose to formulate the heuristic finite volume method with the help of mixed Petrov-Galerkin finite elements. Weighting functions for gradient discretization are parameterized by some function ψ : [0, 1] → R. We propose for this function ψ a compatibility interpolation condition, and we prove that such a condition is equivalent to the inf-sup property when studying stability of the numerical scheme. In the case of stable scheme and under two distinct hypotheses concerning the regularity of the solution, we demonstrate convergence of the finite volume method in appropriate Hilbert spaces and with optimal order of accuracy.

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