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S. Wolff, C. Bucher:
"On continuous assumed gradient elements of second order";
International Journal of Computational Methods (invited), 10 (2013), 01.

This article presents and compares continuous assumed gradient (CAG) methods when applied to structural elasticity. CAG elements are finite elements where the strain, i.e. the deformation gradient, is replaced by a C 0 -continuous interpolation. Similar approaches are found in nodal integration and SFEM. Recently, interpolation schemes for a continuous assumed deformation gradient were proposed for first order tetrahedral and hexahedral finite elements. These schemes try to balance accuracy and numerical efficiency. At the same time the stability of the interpolation with respect to hourglassing and spurious low energy modes is ensured. This article recalls the fundamentals of CAG elements, i.e. the formulation and linearization. Furthermore, it extends the approach to second order finite elements. Examples prove convergence and accuracy of the quadratic elements.
Two interpolation schemes, one being supported by finite element nodes and interior points and the other being a higher-order tensor-product polynomial, are identified to be most accurate.

continuous assumed gradients; nodal integration; assumed gradient; 2nd order; comparison

http://dx.doi.org/10.1142/S0219876213400094

Project Head Christian Bucher:
Formulierung und Test eines glatten zeitadaptiven Raum-Zeit-Integrators