This article discusses computational techniques for simulating natural convection in three-dimensional domains using finite element methods with tetrahedral elements. These techniques form a new numerical procedure for this kind of problems. In this procedure, the treatment of advection by a wave equation approach is extended to three-dimensional unstructured meshes with tetrahedra. Numerical r...

Hierarchical bases of arbitrary order for H(div)-conforming triangular and tetrahedral elements are constructed with the goal of improving the conditioning of the mass and stiffness matrices. For the basis with the triangular element, it is found numerically that the conditioning is acceptable up to the approximation of order four, and is better than a corresponding basis in the dissertation by...

A numerical analysis of the limit state for solids, with an adequately described structural geometry, is often a computationally demanding task, and there need effective method. The existing solid elements Finite Element Limit Analysis (FELA) are either expensive or require stress cutoff yield surface triaxial states. This paper presents partially mixed lower bound tetrahedral constant element ...

• Mixed methods for elastodynamics with weak symmetry. • Mixed finite elements for elasticity on quadrilateral meshes. • Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. • Nonconforming tetrahedral mixed finite elements for elasticity. • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. • ...

On an automatically parallel generation technique for tetrahedral meshes Summary : In order to prepare modern nite element analysis a program for the eecient parallel generation of tetrahedral meshes in a wide class of three dimensional domains having a generalized cylindric shape is presented. The applied mesh generation strategy is based on the decomposition of some 2D-reference domain into s...

This paper deals with topological analysis of sets of tetrahedra (‘‘tetrahedral meshes’’ of three-dimensional objects). We introduce a definition of simple elements for any normal tetrahedral representation. Then we prove a local characterization of simple tetrahedra in the case of a scene composed of one object and its background, based on homology groups and on relative homology. This allows ...

In this paper we apply a nonconforming rotated bilinear tetrahedral element to the Stokes problem in $\mathbb{R}^3$. We show that is stable combination with piecewise linear, continuous, approximation of pressure. This gives an similar well known continuous $P^2-P^1$ Taylor$-$Hood element, but fewer degrees freedom. The non-conforming low order which fulfils Korn's inequality, leading stability...

It is known that piecewise linear continuous finite element (FE) approximations on nonobtuse tetrahedral FE meshes guarantee the validity of discrete analogues of various maximum principles for a wide class of elliptic problems of the second order. Such analogues are often called discrete maximum principles (or DMPs in short). In this work we present several global and local refinement techniqu...

The issue of mesh quality for unstructured triangular and tetrahedral meshes is considered. The theoretical background to finite element methods is used to understand the basis of present-day geometrical mesh quality indicators. Simple tetrahedral mesh quality measures using both geometrical and solution information are described. Some of the issues in mesh quality for unstructured tetrahedral ...