6 papers
Shape Optimization by Constrained First-Order Least Mean Approximation
Gerhard Starke
In this work, the problem of shape optimization, subject to PDE constraints, is reformulated as an best approximation problem under divergence constraints to the shape tensor…
A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem
F. Bertrand, G. Starke
A posteriori error estimates are constructed for the three-field variational formulation of the Biot problem involving the displacements, the total pressure and the fluid pressure.…
Weakly symmetric stress equilibration for hyperelastic materialmodels
Fleurianne Bertrand, Marcel Moldenhauer, Gerhard Starke
A stress equilibration procedure for hyperelastic material models is proposed andanalyzed in this paper. Based on the displacement-pressure approximation computed with a stable fin…
Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity
Fleurianne Bertrand, Bernhard Kober, Marcel Moldenhauer +1
A stress equilibration procedure for linear elasticity is proposed and analyzed in this paper with emphasis on the behavior for (nearly) incompressible materials. Based on the disp…
A posteriori error estimation for planar linear elasticity by stress reconstruction
Fleurianne Bertrand, Marcel Moldenhauer, Gerhard Starke
The nonconforming triangular piecewise quadratic finite element space by Fortin and Soulie can be used for the displacement approximation and its combination with discontinuous pie…
Dev-Div- and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions
Sebastian Bauer, Patrizio Neff, Dirk Pauly +1
For an n-dimensional bounded domain we derive some inequalities bounding the norm of a square tensor field. Concerning the Div-Dev-inequality the bound is given by the trace-free p…