The DPG method for the Stokes problem

Abstract

We discuss well-posedness and convergence theory for the DPG method applied to a general system of linear Partial Differential Equations (PDEs) and specialize the results to the classical Stokes problem. The Stokes problem is an iconic troublemaker for standard Bubnov–Galerkin methods; if discretizations are not carefully designed, they may exhibit non-convergence or locking. By contrast, DPG does not require us to treat the Stokes problem in any special manner. We illustrate and confirm our theoretical convergence estimates with numerical experiments.