34 citations · 113 across the 10 of their papers we have counts for
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A dual singular complement method for the numerical solution of the Poisson equation with boundary data in non-convex domains
Thomas Apel, Serge Nicaise, Johannes Pfefferer
The very weak solution of the Poisson equation with boundary data is defined by the method of transposition. The finite element solution with regularized boundary data conver…
On the regularity of the solutions of Dirichlet optimal control problems in polygonal domains
Thomas Apel, Mariano Mateos, Johannes Pfefferer +1
A linear quadratic Dirichlet control problem posed on a possibly non-convex polygonal domain is analyzed. Detailed regularity results are provided in classical Sobolev (Slobodetski…
Discretization of the Poisson equation with non-smooth data and emphasis on non-convex domains
Thomas Apel, Serge Nicaise, Johannes Pfefferer
Several approaches are discussed how to understand the solution of the Dirichlet problem for the Poisson equation when the Dirichlet data are non-smooth such as if they are in $L^2…