The DPG method for the Stokes problem
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 BubnovGalerkin 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.
stokes problem discontinuous petrovgalerkin