Mixed finite elements for elasticity on quadrilateral meshes

We present the first stable mixed finite elements for plane elasticity on general quadrilateral meshes. The symmetry of the stress tensor is imposed weakly and so there are three primary variables, the stress tensor, the displacement vector field, and the scalar rotation. We develop and analyze a stable family of methods, with one method for each order of convergence greater than one. The methods use Raviart–Thomas elements for the stress, piecewise tensor product polynomials for the displacement, and piecewise polynomials for the rotation, and achieve their given convergence order for all three variables. We also present a simple first order element, not belonging to this family. It uses the lowest order BDM elements for the stress, and piecewise constants for the displacement and rotation, and achieves first order convergence for all three variables.

• Type: Journal
• Year: 2015
• Where: ADCM
• Authors: Douglas N. Arnold, Gerard Awanou, Weifeng Qiu
• Keywords: ADCM 2015, Database