7 papers
Fully discrete best approximation type estimates in for finite element discretizations of the transient Stokes equations
Niklas Behringer, Dmitriy Leykekhman, Boris Vexler
In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discon…
A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system
Marita Holtmannspötter, Arnd Rösch, Boris Vexler
In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradie…
Optimal finite element error estimates for an optimal control problem governed by the wave equation with controls of bounded variation
Sebastian Engel, Philip Trautmann, Boris Vexler
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus l…
Global and local pointwise error estimates for finite element approximations to the Stokes problem on convex polyhedra
Niklas Behringer, Dmitriy Leykekhman, Boris Vexler
The main goal of the paper is to show new stability and localization results for the finite element solution of the Stokes system in and norms under sta…
A sparse control approach to optimal sensor placement in PDE-constrained parameter estimation problems
Ira Neitzel, Konstantin Pieper, Boris Vexler +1
We present a systematic approach to the optimal placement of finitely many sensors in order to infer a finite-dimensional parameter from point evaluations of the solution of an ass…
Numerical Analysis of Sparse Initial Data Identification for Parabolic Problems
Dmitriy Leykekhman, Boris Vexler, Daniel Walter
In this paper we consider a problem of initial data identification from the final time observation for homogeneous parabolic problems. It is well-known that such problems are expon…