Advances and Applications of the Generalized/eXtended Finite Element Method

C. Armando Duarte, University of Illinois at Urbana-Champaign
Patrick O'Hara, Universal Technology Corporation
Julia Plews, Sandia National Laboratories


The Generalized/eXtended Finite Element Method has received increased attention and undergone substantial development during the last decade. This method offers unprecedented flexibility in the construction of shape functions and corresponding approximation spaces. With the proper selection of enrichment functions, this method is able to address many shortcomings and limitations of the classical FEM while retaining its attractive features.
This mini-symposium aims to bring together engineers, mathematicians, computer scientists, and national laboratory and industrial researchers to discuss and exchange ideas on new developments, mathematical analysis, and applications of the Generalized/eXtended Finite Element Method. While contributions to all aspects of this method are invited, featured topics include:

- identification and characterization of problems where the Generalized/eXtended Finite Element Method has a clear advantage over classical approaches;
- applications, such as multi-physics, nonlinear, or contact problems, dislocations, polycrystals, jointed rocks, masonry, composite or biological materials;
- time-dependent problems and stability analysis;
- mathematical theory, including but not limited to a priori and a posteriori error analyses;
- high-order Generalized/eXtended Finite Element Methods; and
- computational implementation aspects, such as imposition of boundary conditions, numerical quadrature, approaches to address conditioning issues with systems of equations arising from this class of methods, adaptive enrichment/refinement algorithms, explicit and implicit representation of moving interfaces.