16 citations · 39 across the 12 of their papers we have counts for
13 papers
The singular Zienkiewicz tetrahedron: Definition and Integration
Johannes Storn
We extend the two-dimensional singular Zienkiewicz element to three dimensions, leading to a novel -conforming finite element on tetrahedral meshes based on rational shape fun…
Dynamical Optimal Transport with -Invariance: From Theory to Computation
Kevine Meugang Toukam, Max von Renesse, Johannes Storn
We introduce a modified Benamou--Brenier (MBB) formulation of optimal transport that incorporates Euclidean invariance at the dynamical level. We establish existence of minimizers…
Examples of -harmonic maps
Anna Balci, Linus Behn, Lars Diening +1
We construct explicit examples of -harmonic maps . These are more irregular than the previously known examples and thus provide new upper bounds…
Guaranteed upper bounds for iteration errors and modified Kacanov schemes via discrete duality
Lars Diening, Johannes Storn
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete…
Exact Integration for singular Zienkiewicz and Guzman-Neilan Finite Elements with Implementation
Lars Diening, Johannes Storn, Tabea Tscherpel
We develop a recursive integration formula for a class of rational polynomials in 2D. Based on this, we present implementations of finite elements that have rational basis function…
Adaptive Mesh Refinement for arbitrary initial Triangulations
Lars Diening, Lukas Gehring, Johannes Storn
We introduce a simple initialization of the Maubach bisection routine for adaptive mesh refinement which applies to any conforming initial triangulation and terminates in linear ti…
Grading of Triangulations Generated by Bisection
Lars Diening, Johannes Storn, Tabea Tscherpel
For triangulations generated by the adaptive bisection algorithm by Maubach and Traxler we prove existence of a regularized mesh function with grading two. This sharpens previous r…
Relaxed Kacanov scheme for the p-Laplacian with large p
Anna Kh. Balci, Lars Diening, Johannes Storn
We introduce a globally convergent relaxed Kacanov scheme for the computation of the discrete minimizer to the -Laplace problem with . The iterative scheme is…
Interpolation Operator on negative Sobolev Spaces
Lars Diening, Johannes Storn, Tabea Tscherpel
We introduce a Scott--Zhang type projection operator mapping to Lagrange elements for arbitrary polynomial order. In addition to the usual properties, this operator is compatible w…
Fortin Operator for the Taylor-Hood Element
Lars Diening, Johannes Storn, Tabea Tscherpel
We design a Fortin operator for the lowest-order Taylor-Hood element in any dimension, which was previously constructed only in 2D. In the construction we use tangential edge bubbl…
A Space-Time DPG Method for the Heat Equation
Lars Diening, Johannes Storn
This paper introduces an ultra-weak space-time DPG method for the heat equation. We prove well-posedness of the variational formulation with broken test functions and verify quasi-…
On the Sobolev and -Stability of the -projection
Lars Diening, Johannes Storn, Tabea Tscherpel
We show stability of the -projection onto Lagrange finite element spaces with respect to (weighted) and -norms for any polynomial degree and for any space dimen…
The parabolic p-Laplacian with fractional differentiability
Dominic Breit, Lars Diening, Johannes Storn +1
We study the parabolic -Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Ou…