It is well known that finite element solutions for elliptic PDEs with Dirac measures as source
terms converge, due to the fact that the solution is not in H^1, suboptimal in classical norms …

In this work we propose and investigate the performance of a metric-based refinement
criteria for adaptive meshing used for improving the numerical solution of an elliptic problem …

The Green function of the Poisson equation in two dimensions is not contained in the
Sobolev space H^1(Ω) such that finite element error estimates for the discretization of a …

We consider elliptic and parabolic variational equations and inequalities governed by
integro-differential operators of order 2s ∈ (0, 2. Our main motivation is the pricing of …

In this article we develop a posteriori error estimates for second order linear elliptic problems
with point sources in two-and three-dimensional domains. We prove a global upper bound …

We discuss the full discretization of an elliptic optimal control problem with pointwise control
and state constraints. We provide the first reliable a-posteriori error estimator that contains …

The solutions of elliptic problems with a Dirac measure right‐hand side are not in dimension
and therefore the convergence of the finite element solutions is suboptimal in the‐norm. In …

In Lipschitz domains, we study a Darcy–Forchheimer problem coupled with a singular heat
equation by a nonlinear forcing term depending on the temperature. By singular we mean …

We establish the existence of liftings into discrete subspaces of H (div) of piecewise
polynomial data on locally refined simplicial partitions of polygonal/polyhedral domains. Our …

In this paper we study the a priori error estimates for the finite element approximations of
parabolic equations with measure data, especially we consider problems with separate …