Minimum residual methods such as the least-squares finite element method (FEM) or the
discontinuous Petrov--Galerkin (DPG) method with optimal test functions usually exclude …

For numerical approximation the reformulation of a PDE as a residual minimisation problem
has the advantages that the resulting linear system is symmetric positive definite, and that …

Local L2-bounded commuting projections in FEEC Page 1 ESAIM: M2AN 55 (2021) 2169–2184
ESAIM: Mathematical Modelling and Numerical Analysis https://doi.org/10.1051/m2an/2021054 …

We consider residual-based a posteriori error estimators for Galerkin discretizations of time-
harmonic Maxwell's equations. We focus on configurations where the frequency is high, or …

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 study variants of the mixed finite element method (mixed FEM) and the first-order system
least-squares finite element (FOSLS) for the Poisson problem where we replace the load by …

We analyze constrained and unconstrained minimization problems on patches of tetrahedra
sharing a common vertex with discontinuous piecewise polynomial data of degree p. We …

We address fundamental aspects in the approximation theory of vector-valued finite element
methods, using finite element exterior calculus as a unifying framework. We generalize the …

We consider an ultra-weak first order system discretization of the Helmholtz equation. When
employing the optimal test norm, the 'ideal'method yields the best approximation to the pair …

We develop commuting finite element projections over smooth Riemannian manifolds. This
extension of finite element exterior calculus establishes the stability and convergence of …