TY - JOUR

T1 - Some remarks on quadrilateral mixed finite elements

AU - Boffi, Daniele

AU - Gastaldi, Lucia

N1 - Generated from Scopus record by KAUST IRTS on 2020-05-05

PY - 2009/6/1

Y1 - 2009/6/1

N2 - 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.

AB - 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.

UR - https://linkinghub.elsevier.com/retrieve/pii/S0045794908002666

UR - http://www.scopus.com/inward/record.url?scp=67349186949&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2008.12.006

DO - 10.1016/j.compstruc.2008.12.006

M3 - Article

SN - 0045-7949

VL - 87

SP - 751

EP - 757

JO - Computers and Structures

JF - Computers and Structures

IS - 11-12

ER -