In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div) − Pk (1 ≤ k ≤ n) tensor spaces, enriched, for each n − 1 dimensional simplex, by (n+1)n 2 H(div) − Pn+1 bubble functions when 1 ≤ k ≤ n − 1, and by (n−1)n 2 H(di...

This book is the third volume of a three-part textbook suitable for both graduate coursework and professional engineering research reference alike. Volume III focuses on time-dependent problems symmetric positive systems first-order PDEs called Friedrichs' systems.

many results were proved on the structure of finite groups with some‎ ‎restrictions on their real elements and on their conjugacy classes‎. ‎we‎ ‎generalize a few of these to some classes of infinite groups‎. ‎we study groups in which real elements are central‎, ‎groups in which real elements are $2$-elements‎, ‎groups in which all non-trivial classes have the same finite size and $fc$-groups w...

starting from two-dimensional (2d) equations of motion, discretized formulations for transient behavior of soil-structure interaction problems have been derived. two different dynamic infinite elements taking into account single and two-wave types are presented in transformed space. by coupling the infinite elements with standard finite elements, an ordinary finite element procedure is used for...

In this paper we present a parallel algorithm of the goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and with parallel multi-frontal direct solver. The algorithm generates in a fully automatic mode (without any user interaction) a sequence of meshes delivering exponential convergence of the prescribed quantity of interest with respect to the mesh size (...

This article introduces a new algorithm for evaluating enrichment functions in the higher-order hierarchical interface-enriched finite element method (HIFEM), which enables the fully mesh-independent simulation of multiphase problems with intricate morphologies. The proposed hierarchical enrichment technique can accurately capture gradient discontinuities along materials interfaces that are in ...