Some remarks on quadrilateral mixed finite elements

Daniele Boffi, Lucia Gastaldi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

It is well known that quadrilateral finite elements may produce unsatisfactory results when used on distorted meshes. It turns out that many commonly used finite elements achieve suboptimal convergence properties on distorted quadrilaterals; among such elements we recall in particular serendipity (trunk) scalar elements and basically all vectorial elements for the approximation of problems involving the functional space H (div) (like Raviart-Thomas or Brezzi-Douglas-Marini spaces for Darcy flow). In two space dimensions, a similar remark applies to edge finite elements for the approximation of Maxwell's problems involving the space H (curl). On the other hand, mimetic finite differences have become popular for the approximation of problems involving H (div) on very general geometries. The aim of this paper is to show how to use the ideas of mimetic finite differences for the stabilization of Raviart-Thomas element on general quadrilateral meshes. It turns out that such stabilization can be performed by a slight modification of the standard Raviart-Thomas element which does not increase significantly the computational cost of the original scheme. © 2008 Elsevier Ltd. All rights reserved.
Original languageEnglish (US)
Pages (from-to)751-757
Number of pages7
JournalComputers and Structures
Volume87
Issue number11-12
DOIs
StatePublished - Jun 1 2009
Externally publishedYes

Fingerprint Dive into the research topics of 'Some remarks on quadrilateral mixed finite elements'. Together they form a unique fingerprint.

Cite this