32 citations · 76 across the 14 of their papers we have counts for
17 papers
Strictly equivalent a~posteriori error estimators for quasi-optimal nonconforming methods
Christian Kreuzer, Matthias Rott, Andreas Veeser +1
We devise a posteriori error estimators for quasi-optimal nonconforming finite element methods approximating symmetric elliptic problems of second and fourth order. These estimator…
Pressure robust finite element discretizations of the nonlinear Stokes equations
Lars Diening, Adrian Hirn, Christian Kreuzer +1
We present first-order nonconforming Crouzeix-Raviart discretizations for the nonlinear generalized Stokes equations with -structure. Thereby the velocity-errors are indepen…
Inf-sup theory for the quasi-static Biot's equations in poroelasticity
C. Kreuzer, P. Zanotti
We analyze the two-field formulation of the quasi-static Biot's equations in bounded domains by means of the inf-sup theory. For this purpose, we exploit an equivalent four-field f…
On the threshold condition for Dörfler marking
Lars Diening, Christian Kreuzer
It is an open question if the threshold condition for the Dörfler marking parameter is necessary to obtain optimal algebraic rates of adaptive finite element methods.…
Quasi-optimal and pressure robust discretizations of the Stokes equations by moment- and divergence-preserving operators
Christian Kreuzer, Rüdiger Verfürth, Pietro Zanotti
We approximate the solution of the Stokes equations by a new quasi-optimal and pressure robust discontinuous Galerkin discretization of arbitrary order. This means quasi-optimality…
Convergence of an adaptive -interior penalty Galerkin method for the biharmonic problem
Alexander Dominicus, Fernando Gaspoz, Christian Kreuzer
We develop a basic convergence analysis for an adaptive method for the Biharmonic problem, which provides convergence without rates for all practically r…
Convergence of adaptive discontinuous Galerkin methods (corrected version of [Math. Comp. 87 (2018), no. 314, 2611--2640])
Christian Kreuzer, Emmanuil H. Georgoulis
We develop a general convergence theory for adaptive discontinuous Galerkin methods for elliptic PDEs covering the popular SIPG, NIPG and LDG schemes as well as all practically rel…
Quasi-best approximation in optimization with PDE constraints
Fernando Gaspoz, Christian Kreuzer, Andreas Veeser +1
We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting th…
Oscillation in a posteriori error estimation
Christian Kreuzer, Andreas Veeser
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to re…
Quasi-optimal and pressure robust discretizations of the Stokes equations by new augmented Lagrangian formulations
Christian Kreuzer, Pietro Zanotti
We approximate the solution of the stationary Stokes equations with various conforming and nonconforming inf-sup stable pairs of finite element spaces on simplicial meshes. Based o…
A convergent time-space adaptive dG(s) finite element method for parabolic problems motivated by equal error distribution
Fernando Gaspoz, Christian Kreuzer, Kunibert Siebert +1
We shall develop a fully discrete space-time adaptive method for linear parabolic problems based on new reliable and efficient a posteriori analysis for higher order dG(s) finite e…
Adaptive Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology
Christian Kreuzer, Endre Süli
We develop the a posteriori error analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric…
Instance optimal Crouzeix-Raviart adaptive finite element methods for the Poisson and Stokes problems
Christian Kreuzer, Mira Schedensack
We extend the ideas of Diening, Kreuzer, and Stevenson [Instance optimality of the adaptive maximum strategy, Found. Comput. Math. (2015)], from conforming approximations of the Po…
Instance optimality of the adaptive maximum strategy
Lars Diening, Christian Kreuzer, Rob Stevenson
In this paper, we prove that the standard adaptive finite element method with a (modified) `maximum marking strategy' is `instance optimal' for the `total error', being the sum of…
Convex Hull Property and Maximum Principle for Finite Element Minimisers of General Convex Functionals
Lars Diening, Christian Kreuzer, Sebastian Schwarzacher
The convex hull property is the natural generalization of maximum principles from scalar to vector valued functions. Maximum principles for finite element approximations are often…
A Note on why Enforcing Discrete Maximum Principles by a simple a Posteriori Cutoff is a Good Idea
Christian Kreuzer
Discrete maximum principles in the approximation of partial differential equations are crucial for the preservation of qualitative properties of physical models. In this work we en…
Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology
Lars Diening, Christian Kreuzer, Endre Süli
We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the veloci…