August Johansson

TL;DR: The FEniCS Project is a collaborative project for the development of innovative concepts and tools for automated scientific computing, with a particular focus on the solution of differential equations by finite element methods.

TL;DR: This work proposes a discontinuous Galerkin method that avoids using very small elements on the boundary by associating them to a neighboring element with a sufficiently large intersection with the domain, and proves the crucial inverse inequality that leads to a coercive bilinear form.

TL;DR: In this article, a new framework for expressing finite element methods on multiple intersecting meshes is presented, which enables the use of separate meshes to discretize the finite element method.

TL;DR: An adaptive algorithm for evolution problems that employs a sequence of “blocks” consisting of fixed, though nonuniform, space meshes that offers the advantages of adaptive mesh refinement but with reduced overhead costs associated with load balancing, remeshing, matrix reassembly, and the solution of adjoint problems used to estimate discretization error and the effects of mesh changes is described.

TL;DR: A high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces based on a Nitsche formulation of the interface condition together with a stabilization term is developed.