The use of finite element (FE) analysis in the simulation of physical phenomena over the human body has necessitated the construction of meshes from images. Despite the availability of several tools for generating meshes for FE-based applications, most cannot deal directly with the raw pixel-wise representation of image data. Additionally, some are optimized for the construction of much simpler...

The introduction of the Quadrilateral Area Coordinate (QAC) membrane elements has generated more heat than light on the subject of why distorted membrane elements perform very poorly. The canonical guidelines for construction of robust elements are continuity and completeness. It is known that isoparametric (or parametric) quadrilateral membrane elements satisfy the continuity requirements alwa...

We prove convergence and optimal complexity of an adaptive finite element algorithm on quadrilateral meshes. The local mesh refinement algorithm is based on regular subdivision of marked cells, leading to meshes with hanging nodes. In order to avoid multiple layers of these, a simple rule is defined, which leads to additional refinement. We prove an estimate for the complexity of this refinemen...

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 ...

where f ∈ L2(Ω). Let Th be a simplicial or convex quadrilateral triangulation of Ω. In C 0 interior penalty methods, we choose the discrete space Vh ⊂ H 1 0 (Ω) to be either a P` (` ≥ 2) triangular Lagrange finite element space or a Q` (` ≥ 2) tensor product finite element space associated with Th. By an integration by parts argument [4], it can be shown that the solution u of (1), which belong...

We present techniques of a posteriori error estimation for Q1 finite element discretizations based on residual evaluations with respect to test functions of higher-order. This technique is designed for quadrilateral (or hexahedral) triangulations and gives local error indicators in terms of nodal contributions. We show reliability and efficiency of the estimator. Moreover, we present a simplifi...