The accuracy of Finite Element approximation depends on the size and shape of elements. The proposed theory clarifies the source of shape related errors. A new general accuracy condition based on the maximum eigenvalue of the element stiffness matrix (or, alternatively, its trace) is presented. Several new and several familiar geometric criteria follow directly from the eigenvalue condition as ...

We present new finite element methods for Helmholtz and Maxwell equations for general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coeffic...

This paper presents finite element computation for brain deformation during craniotomy. The results are used to illustrate the comparison between two mechanical models: linear solid-mechanic model, and non linear finite element model. To this end, we use a test sphere as a model of the brain, tetrahedral finite element mesh, two models that describe the material property of the brain tissue, an...

A new approach of constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed The linear system arising from the mixed methods is rst algebraically condensed to a symmetric positive de nite system for Lagrange multipliers which corresponds to a linear system generated by standard nonco...

One of the key factors for obtaining accurate and reliable results using the Finite Element Method (FEM) is the discretization of the domain. Traditionally, two main types of elements are used for three-dimensional mesh generation: tetrahedral and hexahedral elements. Tetrahedral meshes are automatically generated but standard displacement-based tetrahedral elements generally suffer from perfor...

Local transformation, or topological reconnection, is one of effective procedures of mesh improvement method, especially for three-dimensional tetrahedral mesh. Although the existing local transformations such as 2-3/3-2 flip are effective in removing poorly-shaped tetrahedra, it is still possible to improve the quality of mesh further by expanding the space of transformation region. The author...