2018/11/02 by Ilona Ambartsumyan, Eldar Khattatov, Ambartsumyan, Ilona +5
Engineering · #Advanced Numerical Methods in Computational Mathematics #Elasticity and Material Modeling #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1811.01928
openalex publication_date 2018/11/02 · openalex created_date 2022/08/02 · openalex updated_date 2026/07/28
We develop a multipoint stress mixed finite element method for linear\nelasticity with weak stress symmetry on quadrilateral grids, which can be\nreduced to a symmetric and positive definite cell centered system. The method\nis developed on simplicial grids in [4]. The method utilizes the lowest order\nBrezzi-Douglas-Marini finite element spaces for the stress and the trapezoidal\nquadrature rule in order to localize the interaction of degrees of freedom,\nwhich allows for local stress elimination around each vertex. We develop two\nvariants of the method. The first uses a piecewise constant rotation and\nresults in a cell-centered system for displacement and rotation. The second\nuses a continuous piecewise bilinear rotation and trapezoidal quadrature rule\nfor the asymmetry bilinear form. This allows for further elimination of the\nrotation, resulting in a cell-centered system for the displacement only.\nStability and error analysis is performed for both methods. First-order\nconvergence is established for all variables in their natural norms. A duality\nargument is employed to prove second order superconvergence of the displacement\nat the cell centers. Numerical results are presented in confirmation of the\ntheory.\n