An Alternative to the Least-Squares Mixed Finite Element Method for Elliptic Problems

Jan Brandts () and Yanping Chen ()
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Jan Brandts: University of Amsterdam, Korteweg-de Vries Institute for Mathematics, Faculty of Science
Yanping Chen: Xiangtan University, Department of Mathematics

A chapter in Numerical Mathematics and Advanced Applications, 2004, pp 169-175 from Springer

Abstract: Summary In this paper we derive a strengthened Cauchy-Schwarz inequality that enables us to formulate a short and transparant proof of the coercivity of a Least Squares Mixed Finite Element bilinear form. Also, it shows that the coupling between H 0 1 (Ω) and H(div; Ω) is weak enough to be neglected. This results in an alternative way to compute approximations of both the scalar variable and its gradient for second order elliptic problems.

Keywords: Elliptic Problem; Finite Element Space; Order Elliptic Problem; MultiGrid Solver; High Order Perturbation (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18775-9_14

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DOI: 10.1007/978-3-642-18775-9_14

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