5 papers
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…
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…
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…
Non-coercive Neumann boundary control problems
Thomas Apel, Mariano Mateos, Arnd Rösch
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-st…
-error estimates for Neumann boundary value problems on graded meshes
Thomas Apel, Johannes Pfefferer, Sergejs Rogovs +1
This paper deals with a priori pointwise error estimates for the finite element solution of boundary value problems with Neumann boundary conditions in polygonal domains. Due to th…