2017/10/19 by da Veiga, Lourenço Beirão, Mora, David, Rivera, Gonzalo · 3 citations
#65N12 #65N15 (Primary) #65N30 #74K20 #74S05 #FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.1710.07330
We present a virtual element method for the Reissner-Mindlin plate bending problem which uses shear strain and deflection as discrete variables without the need of any reduction operator. The proposed method is conforming in [H1(Ω)]2 × H2(Ω) and has the advantages of using general polygonal meshes and yielding a direct approximation of the shear strains. The rotations are then obtained by a simple postprocess from the shear strain and deflection. We prove convergence estimates with involved constants that are uniform in the thickness t of the plate. Finally, we report numerical experiments which allow us to assess the performance of the method.