3 citations · 4 across the 9 of their papers we have counts for
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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…
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…