A two-dimensional mixed finite-element pair on rectangles

2013 ◽  
Vol 140 (680) ◽  
pp. 930-942 ◽  
Author(s):  
Thomas Melvin ◽  
Andrew Staniforth ◽  
Colin Cotter
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Two Dimensional ◽  
Element Pair

A CONSTRUCTION OF SPACES OF COMPATIBLE DIFFERENTIAL FORMS ON CELLULAR COMPLEXES

2008 ◽  
Vol 18 (05) ◽  
pp. 739-757 ◽  
Author(s):  
SNORRE H. CHRISTIANSEN
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Differential Forms ◽  
Cochain Complex ◽  
Two Dimensional ◽  
Exterior Derivative ◽  
Whitney Forms ◽  
Reconstruction Operator ◽  
Mimetic Finite Differences ◽  
Cellular Complex

Given a cellular complex, we construct spaces of differential forms which form a complex under the exterior derivative, which is isomorphic to the cochain complex of the cellular complex. The construction applies in particular to subsets of Euclidean space divided into polyhedra, for which it provides, for each k, a space of k-forms with a basis indexed by the set of k-dimensional cells. In the framework of mimetic finite differences, the construction provides a conforming reconstruction operator. The construction requires auxiliary spaces of differential forms on each cell, for which we provide two examples. When the cells are simplexes, the construction can be used to recover the standard mixed finite element spaces also called Whitney forms. We can also recover the dual finite elements previously constructed by A. Buffa and the author on the barycentric refinement of a two-dimensional mesh.

scholarly journals Two dimensional mixed finite element approximations for elliptic problems with enhanced accuracy for the potential and flux divergence

2017 ◽  
Vol 74 (12) ◽  
pp. 3283-3295 ◽  
Author(s):  
Agnaldo M. Farias ◽  
Philippe R.B. Devloo ◽  
Sônia M. Gomes ◽  
Denise de Siqueira ◽  
Douglas A. Castro
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Elliptic Problems ◽  
Two Dimensional ◽  
Flux Divergence ◽  
Finite Element Approximations

scholarly journals Enriched two dimensional mixed finite element models for linear elasticity with weak stress symmetry

2020 ◽  
Vol 79 (9) ◽  
pp. 2678-2700
Author(s):  
Philippe R.B. Devloo ◽  
Sônia M. Gomes ◽  
Thiago O. Quinelato ◽  
Shudan Tian
Keyword(s):  
Finite Element ◽  
Linear Elasticity ◽  
Mixed Finite Element ◽  
Finite Element Models ◽  
Two Dimensional
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