Diamond shaped stent 

Associated people

J. Schröder, A. Schwarz, K.Steeger, in cooperation with G. Starke (Leibniz University Hannover)

Abstract

For the solution of partial differential equations describing physical problems in the framework of solid mechanics, we develop in this project least-squares mixed finite element formulations and examine their performance. Starting from the balance of momentum, we obtain div-grad first-order systems with e.g. stresses and displacements as unknowns and by means of quadratic L₂-norms a least-squares functional can be constructed. This functional is the basis for the associated minimization problem, which is not restricted to the LBB-condition. Moreover, due to some additional advantages, as e.g. a smooth stress approximation even for quasi-incompressible materials and an a posteriori error estimator without additional costs, least-squares variational principles have increasingly gained attention. 

References

Schwarz, A., Schröder, J. & Starke, G. [2010], “A modified Least-Squares Mixed Finite Element with improved Momentum Balance”, International Journal for Numerical Methods in Engineering 81, p. 286-306.

Schwarz, A. [2009], “Least-Squares Mixed Finite Elements for Solid Mechanics”, Dissertation, Institut für Mechanik, Bericht 7, Universität Duisburg-Essen.

Schwarz, A., Schröder, J. & Starke, G. [2009], “Least-Squares Mixed Finite Elements for Small Strain Elasto-Viscoplasticity”, International Journal for Numerical Methods in Engineering 77, p. 1351-1370.