This article presents the major mathematical and implementation features of a weak form
language (GWFL) for an automated finite-element (FE) solution of partial differential …

In this paper, we discuss how to efficiently evaluate and assemble general finite element
variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of …

A computational homogenization method to determine the effective parameters of Mindlin's
Strain Gradient Elasticity (SGE) model from a local heterogeneous Cauchy linear material is …

The interior transmission problem is a boundary value problem that arises in the scattering
of time-harmonic waves by an inhomogeneous medium of compact support. The associated …

In the present work, a numerical finite element framework is introduced to model and solve
the response of nonlinear soft dielectrics, including the effects of Maxwell stress and …

Many classical finite elements such as the Argyris and Bell elements have long been absent
from high-level PDE software. Building on recent theoretical work, we describe how to …

This paper presents a conforming finite element discretization of the streamfunction
formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly …

This paper is concerned with the finite element approximation of the stochastic Cahn–
Hilliard–Cook equation driven by an infinite dimensional Wiener type noise. The Argyris …

This chapter provides a glimpse of the considerable range of finite elements in the literature.
Many of the elements presented here are implemented as part of the FEniCS project …

The use of a reference element on which a finite element basis is constructed once and
mapped to each cell in a mesh greatly expedites the structure and efficiency of finite element …