A Numerical Study of a Weakly Symmetric Dual‐Mixed Finite Element Method for the Stokes Source Problem With Velocity Postprocessing

ABSTRACT We present a numerical study of a weakly symmetric dual‐mixed finite element method for the Stokes source problem, in which the Cauchy stress is the primary unknown and its symmetry is imposed weakly through a vorticity Lagrange multiplier. Viewing the scheme as the incompressible limit of the reduced‐symmetry mixed elasticity framework, we employ the Raviart–Thomas based family , which approximates stress, velocity and vorticity to the uniform order . We recall the corresponding a priori error estimates and a local velocity postprocessing that superconverges with order , and we describe the hybridisation and element‐wise static condensation that the balanced family admits, which retains a single piecewise‐constant pressure unknown per element and reduces the globally coupled system to between roughly and of its full size in both two and three dimensions. All estimates are illustrated by numerical experiments on the unit square and the unit cube. The formulation also provides the basis for the stress‐based Stokes eigenvalue problem we treat in forthcoming work.