2013/06/28 by Douglas N. Arnold, Arnold, Douglas N., Gerard Awanou +3
Computer Science · Engineering · #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1306.6821
openalex publication_date 2013/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present stable mixed finite elements for planar linear 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, indexed by an integer r ≥ 2 and with rate of convergence in the L2 norm of order r for all the variables. The methods use Raviart-Thomas elements for the stress, piecewise tensor product polynomials for the displacement, and piecewise polynomials for the rotation. 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.