The FEniCS Project set out in 2003 with an idea to automate the solution of mathematical
models based on differential equations. Initially, the FEniCS Project consisted of two …

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the
most successful domain decomposition solvers for partial differential equations. The …

In this dissertation, we investigate the variational solution to fractional partial differential
equations. The fractional advection dispersion equation models the anomalous diffusive …

We present various results on the equivalence and mapping properties under affine
transformations of fractional-order Sobolev norms and semi-norms of orders between zero …

We consider multilevel decompositions of piecewise constants on simplicial meshes that are
stable in $ H^{-s} $ for $ s\in (0, 1) $. Proofs are given in the case of uniformly and locally …

We investigate a time‐domain Galerkin boundary element method for the wave equation
outside a Lipschitz obstacle in an absorbing half‐space. A priori estimates are presented for …

In bounded domains, the regularity of the solutions to boundary value problems depends on
the geometry, and on the coefficients that enter into the definition of the model. This is in …

We introduce and analyze a Nitsche-based domain decomposition method for the solution
of hypersingular integral equations. This method allows for discretizations with non …

We present an adaptive refinement strategy for the h-version of the boundary element
method with weakly singular operators on surfaces. The model problem deals with the …

We present an a priori analysis of the hp-version of the finite element method for the primal–
dual formulation of frictional contact in linear elasticity. We employ a novel hp-mortar …