Nonstandard Finite Element Methods

Abstract

After just over half a century of use, finite element methods are ubiquitous in engineering (where they were first developed) and science. The mathematical analysis of standard conforming finite elements is very well advanced giving rise to highly efficient codes particularly for elliptic problems. More recently, to improve robustness, computational aspects or to provide extra properties (e.g. appropriate conservation properties) new finite element methods such as discontinuous Galerkin methods, generalized finite element methods and high order methods have been developed. These “non-standard” finite element methods are the subject of this Oberwolfach workshop. The extended abstracts here represent a snapshot of a varied and quickly evolving field.