34 citations · 113 across the 11 of their papers we have counts for
14 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…
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…
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…
Finite element error estimates in for regularized discrete approximations to the obstacle problem
Dominik Hafemeyer, Christian Kahle, Johannes Pfefferer
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the -norm. The discrete approximations are introduced as solution…
-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…
-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…
Error estimates for Dirichlet control problems in polygonal domains
Thomas Apel, Mariano Mateos, Johannes Pfefferer +1
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the a…
Fractional Operators with Inhomogeneous Boundary Conditions: Analysis, Control, and Discretization
Harbir Antil, Johannes Pfefferer, Sergejs Rogovs
In this paper we introduce new characterizations of spectral fractional Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical cases with…
A note on semilinear fractional elliptic equation: analysis and discretization
Harbir Antil, Johannes Pfefferer, Mahamadi Warma
In this paper we study existence, regularity, and approximation of solution to a fractional semilinear elliptic equation of order . We identify minimal conditions on t…
Adapted numerical methods 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…
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…
Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations
Johannes Pfefferer, Klaus Krumbiegel
This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the con…