A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids

A Family of Conforming Mixed Finite Elements for Linear Elasticity on Triangular Grids

This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full C0-Pk space enriched by (k − 1) H(div) edge bubble functions on each internal edge, while the displacement field by the full discontinuous Pk−1 vector-valued...

Mixed Finite Elements as Finite Differences for Elliptic Equations on Triangular Elements

Divergence-free finite elements on tetrahedral grids for k≥6

It was shown two decades ago that the Pk-Pk−1 mixed element on triangular grids, approximating the velocity by the continuous Pk piecewise polynomials and the pressure by the discontinuous Pk−1 piecewise polynomials, is stable for all k ≥ 4, provided the grids are free of a nearly-singular vertex. The problem with the method in 3D was posted then and remains open. The problem is solved partiall...

Nonconforming Tetrahedral Mixed Finite Elements for Elasticity

This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, an...

A family of 3D continuously differentiable finite elements on tetrahedral grids

A family of continuously differentiable piecewise polynomials of degree 9 and higher, on general tetrahedral grids, is constructed, by simplifying and extending the P9 element of Ženǐsek. A mathematical justification and numerical tests are presented. The current computing power is still limited for the computation with 3D C1 finite elements in general. The construction here mainly serves the p...