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Sobolev stability of the -projection on hybrid meshes
Lars Diening, Viktoria Lingert, Tabea Tscherpel
We establish - and -stability of the -projection onto mapped Lagrange finite elements on hybrid meshes consisting of triangles and convex quadrilaterals arising…
A quasi-optimal space-time FEM with local mesh refinements for parabolic problems
Lars Diening, Rob Stevenson, Johannes Storn
We present a space-time finite element method for the heat equation that computes quasi-optimal approximations with respect to natural norms while incorporating local mesh refineme…
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…
Numerical approximation of variational problems with orthotropic growth
Anna Kh. Balci, Lars Diening, Abner J. Salgado
We consider the numerical approximation of variational problems with orthotropic growth, that is those where the integrand depends strongly on the coordinate directions with possib…