3 papers
math.NA2026
Numerical analysis for the Stokes problem with non-homogeneous Dirichlet boundary condition
Thomas Apel, Katharina Lorenz, Johannes Pfefferer
The Stokes problem with non-homogeneous Dirichlet boundary condition is solved numerically using conforming discretizations and an approximation of the boundary datum in the corres…
math.OC2026
Dirichlet control problems with energy regularization governed by non-coercive elliptic equations
Thomas Apel, Mariano Mateos, Arnd Rösch
The present study investigates a linear-quadratic Dirichlet control problem governed by a non-coercive elliptic equation posed on a possibly non-convex polygonal domain. Tikhonov r…
math.NA2025
Weak and very weak solutions of the Laplace equation and the Stokes system with prescribed regularity
Thomas Apel, Katharina Lorenz, Serge Nicaise
To verify theoretical results it is sometimes important to use a numerical example where the solution has a particular regularity. The paper describes one approach to construct suc…