6 citations · 18 across the 22 of their papers we have counts for
16 papers · 1 filter
Variational problems with gradient constraints: and error identities
Harbir Antil, Sören Bartels, Alex Kaltenbach +1
In this paper, on the basis of a (Fenchel) duality theory on the continuous level, we derive an error identity for arbitrary conforming approximations of a…
and error identities for the scalar Signorini problem
Sören Bartels, Thirupathi Gudi, Alex Kaltenbach
In this paper, on the basis of a (Fenchel) duality theory on the continuous level, we derive an error identity for arbitrary conforming approximations of th…
Exact a posteriori error control for variational problems via convex duality and explicit flux reconstruction
Sören Bartels, Alex Kaltenbach
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to estab…
Quasi-optimal Discontinuous Galerkin discretisations of the -Dirichlet problem
J. Blechta, P. A. Gazca-Orozco, A. Kaltenbach +1
The classical arguments employed when obtaining error estimates of Finite Element (FE) discretisations of elliptic problems lead to more restrictive assumptions on the regularity o…
Explicit a posteriori error representation for variational problems and application to TV-minimization
Sören Bartels, Alex Kaltenbach
In this paper, we propose a general approach for explicit a posteriori error representation for convex minimization problems using basic convex duality relations. Exploiting discre…
Error analysis for a Crouzeix-Raviart approximation of the variable exponent Dirichlet problem
Anna Kh. Balci, Alex Kaltenbach
In the present paper, we examine a Crouzeix-Raviart approximation of the -Dirichlet problem. We derive a error estimate, , a best-approxi…
Error analysis for a Crouzeix-Raviart approximation of the obstacle problem
Sören Bartels, Alex Kaltenbach
In the present paper, we study a Crouzeix-Raviart approximation of the obstacle problem, which imposes the obstacle constraint in the midpoints (i.e., barycenters) of the elements…
Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications
Alex Kaltenbach, Michael Růžička
In this paper, we consider a fully-discrete approximation of an abstract evolution equation deploying a non-conforming spatial approximation and finite differences in time (Rothe-G…
Error analysis for a Crouzeix-Raviart approximation of the -Dirichlet problem
Alex Kaltenbach
In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a -structure for some and .…
A Local Discontinuous Galerkin approximation for the -Navier-Stokes system, Part III: Convergence rates for the pressure
Alex Kaltenbach, Michael Růžička
In the present paper, we prove convergence rates for the pressure of the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, of systems of -Navier…
A Local Discontinuous Galerkin approximation for the -Navier-Stokes system, Part II: Convergence rates for the velocity
Alex Kaltenbach, Michael Růžička
In the present paper, we prove convergence rates for the Local Discontinuous Galerkin (LDG) approximation, proposed in Part I of the paper, for systems of -Navier-Stokes type an…
A Local Discontinuous Galerkin approximation for the -Navier-Stokes system, Part I: Convergence analysis
Alex Kaltenbach, Michael Růžička
In the present paper, we propose a Local Discontinuous Galerkin (LDG) approximation for fully non-homogeneous systems of -Navier-Stokes type. On the basis of the primal formulat…
The Deep Ritz Method for Parametric -Dirichlet Problems
Alex Kaltenbach, Marius Zeinhofer
We establish error estimates for the approximation of parametric -Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries an…
Explicit and efficient error estimation for convex minimization problems
Sören Bartels, Alex Kaltenbach
We combine a systematic approach for deriving general a posteriori error estimates for convex minimization problems based on convex duality relations with a recently derived genera…
Convergence analysis of a Local Discontinuous Galerkin approximation for nonlinear systems with balanced Orlicz-structure
Alex Kaltenbach, Michael Růžička
In this paper, we investigate a Local Discontinuous Galerkin (LDG) approximation for systems with balanced Orlicz-structure. We propose a new numerical flux, which yields optimal c…
Error estimates for total-variation regularized minimization problems with singular dual solutions
Alex Kaltenbach, Sören Bartels
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems using the Crouzeix--Raviart finite element require th…