Solution of nearly incompressible field problems using a generalized finite element approach

It is well known that for problems approaching incompressible limits, standard finite element approaches suffer from suboptimal convergence due to a phenomenon known as locking. We analyze this phenomenon and present a robust generalized finite element formulation that enables optimal solution convergence. This approach is explored for the two-dimensional incompressible elasticity equations with a variable Poisson’s ratio, as well as the two-dimensional lid-driven cavity Stokes flow problem using a penalty pressure formulation. •GFEM naturally mitigates the effect of locking as the incompressible limit is approached.•Robust approach for solving incompressible field problems, enabling high-order solution convergence.•GFEM solution presented for 2D incompressible elasticity equations, and 2D lid-driven cavity Stokes flow.