Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties, and numerical experiments

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24220%2F05%3A00000061" target="_blank" >RIV/46747885:24220/05:00000061 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Equivalence between lowest-order mixed finite element and multi-point finite volume methods. Derivation, properties, and numerical experiments
Original language description
We consider the lowest-order Raviart--Thomas mixed finite element method for elliptic diffusion problems on simplicial meshes in two or three space dimensions. This method produces saddle-point problems for scalar and flux unknowns.We show how to easilyeliminate the flux unknowns, which implies an equivalence between this method and a particular multi-point finite volume scheme, without any approximate numerical integration.The matrix of the final linear system is sparse, positive definite for a largeclass of problems, but in general nonsymmetric. We next show that these ideas also apply to mixed and upwinconvection--reaction--diffusion problems. We finally present a set of numerical experiments confirming important computational savings while usingthe equivalent finite volume form of the lowest-order mixed finite element method.
Czech name
Ekvivalence mezi smíšenou metodou konečných prvků nejnižšího stupně a ícebodové metody konečných objemů. Odvození, vlastnosti a numerické expe
Czech description
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Project
<a href="/en/project/1M0554" target="_blank" >1M0554: Advanced Remedial Technologies and Processes</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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