We describe here a library aimed at automating the solution of partial differential equations
using the finite element method. By employing novel techniques for automated code …

We give an overview of open source finite element software Elmer which has initially been
developed by having especially multiphysics simulations in mind. We emphasize the role of …

This textbook teaches finite element methods from a computational point of view. It focuses
on how to develop flexible computer programs with Python, a programming language in …

In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM)
framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast …

A DISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE AND
THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL …

This self-tutorial offers a concise yet thorough grounding in the mathematics necessary for
successfully applying FEMs to practical problems in science and engineering. The unique …

This book presents a systematic methodology for the development of parallel multi-physics
models and its implementation in geophysical and biomedical applications. The …

Firedrake is a new tool for automating the numerical solution of partial differential equations.
Firedrake adopts the domain-specific language for the finite element method of the FEniCS …

In this paper, we propose oversampling strategies in the generalized multiscale finite
element method (GMsFEM) framework. The GMsFEM, which has been recently introduced …

A finite difference method on an unstructured finite element mesh which we call finite
difference element method (FDEM) is presented. The FDEM program package will be a …