44 citations · 202 across the 26 of their papers we have counts for
28 papers
Fully discrete error analysis of finite element discretizations of time-dependent Stokes equations in a stream-function formulation
Dmitriy Leykekhman, Boris Vexler, Jakob Wagner
In this paper we establish best approximation type error estimates for the fully discrete Galerkin solutions of the time-dependent Stokes problem using the stream-function formulat…
Optimal Control of the Navier-Stokes equations via Pressure Boundary Conditions
Boris Vexler, Jakob Wagner
In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary cond…
A priori error estimates for finite element discretization of semilinear elliptic equations with non-Lipschitz nonlinearities
Boris Vexler
In this paper we develop numerical analysis for finite element discretization of semilinear elliptic equations with potentially non-Lipschitz nonlinearites. The nonlinearity is ess…
Numerical Analysis for Neumann Optimal Control Problems on Convex Polyhedral Domains
Johannes Pfefferer, Boris Vexler
This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are cons…
A priori error estimates for optimal control problems governed by the transient Stokes equations and subject to state constraints pointwise in time
Dmitriy Leykekhman, Boris Vexler, Jakob Wagner
In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which…
Numerical Analysis for Dirichlet Optimal Control Problems on Convex Polyhedral Domains
Johannes Pfefferer, Boris Vexler
In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are…
Error estimates for finite element discretizations of the instationary Navier-Stokes equations
Boris Vexler, Jakob Wagner
In this work we consider the two dimensional instationary Navier-Stokes equations with homogeneous Dirichlet/no-slip boundary conditions. We show error estimates for the fully disc…
and best approximation type error estimates for Galerkin solutions of transient Stokes problems
Dmitriy Leykekhman, Boris Vexler
In this paper we establish best approximation type estimates for the fully discrete Galerkin solutions of transient Stokes problem in and norms.…
Fully Discrete Pointwise Smoothing Error Estimates for Measure Valued Initial Data
Dmitriy Leykekhman, Boris Vexler, Jakob Wagner
In this paper we analyze a homogeneous parabolic problem with initial data in the space of regular Borel measures. The problem is discretized in time with a discontinuous Galerkin…
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…
Finite element error estimates for one-dimensional elliptic optimal control by BV functions
Dominik Hafemeyer, Florian Mannel, Ira Neitzel +1
We consider an optimal control problem governed by a one-dimensional elliptic equation that involves univariate functions of bounded variation as controls. For the discretization o…
Error estimates for space-time discretization of parabolic time-optimal control problems with bang-bang controls
Lucas Bonifacius, Konstantin Pieper, Boris Vexler
In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time an…
Finite Element Error Estimates for Optimal Control Problems with Pointwise Tracking
Niklas Behringer, Dominik Meidner, Boris Vexler
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming…
A priori Error Estimates for Space-Time Finite Element Discretization of Parabolic Time-Optimal Control Problems
Lucas Bonifacius, Konstantin Pieper, Boris Vexler
Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a…
Discrete maximal parabolic regularity for Galerkin finite element methods for non-autonomous parabolic problem s
Dmitriy Leykekhman, Boris Vexler
The main goal of the paper is to establish time semidiscrete and space-time fully discrete maximal parabolic regularity for the lowest order time discontinuous Galerkin solution of…
Optimal Error Estimates for Fully Discrete Galerkin Approximations of Semilinear Parabolic Equations
Dominik Meidner, Boris Vexler
We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0)…
-Finite Elements for Fractional Diffusion
Dominik Meidner, Johannes Pfefferer, Klemens Schürholz +1
The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is ba…
Finite element error analysis for measure-valued optimal control problems governed by a 1D wave equation with variable coefficients
Philip Trautmann, Boris Vexler, Alexander Zlotnik
This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces of either measure-valued fu…
Optimal a priori error estimates of parabolic optimal control problems with a moving point control
Dmitriy Leykekhman, Boris Vexler
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise c…