Stabilized mixed triangular finite elements at large deformations using area bubble functions

Symmetric and conforming mixed finite elements for plane elasticity using rational bubble functions

The date of receipt and acceptance will be inserted by the editor Summary We construct stable, conforming and symmetric finite elements for the mixed formulation of the linear elasticity problem in two dimensions. In our approach we add three divergence free rational functions to piecewise polynomials to form the stress finite element space. The relation with the elasticity elements and a class...

Bubble Functions Prompt Unusual Stabilized Finite Element Methods

A second order linear scalar diierential equation including a zero-th order term is approximated using rst the standard Galerkin method enriched with bubble functions. Static condensation of the bubbles suggest an unusual stabilized nite element method for which we establish a convergence study and obtain successful numerical simulations. The method is generalized to allow for a convection oper...

Superconvergence for Second Order Triangular Mixed and Standard Finite Elements

JYV ASKYL A 1996 2 Superconvergence for second order triangular mixed and standard nite elements. Abstract In this paper we will prove that both the second order Raviart-Thomas type mixed nite elements and the quadratic standard nite elements on regular and uniform triangular partitions, are superconvergent with respect to Fortin interpolation. This result implies the superconvergence for quadr...

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

On the stability of bubble functions and a stabilized mixed finite element formulation for the Stokes problem

In this paper we investigate the relationship between stabilized and enriched finite element formulations for the Stokes problem. We also present a new stabilized mixed formulation for which the stability parameter is derived purely by the method of weighted residuals. This new formulation allows equal order interpolation for the velocity and pressure fields. Finally, we show by counterexample ...