A DPG method for the streamfunction formulation of Stokes equations
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In this talk we present recent results on the discontinuous Petrov–Galerkin method for solving Stokes equations in streamfunction formulation in two dimensions. We consider an ultra-weak formulation and discuss basic properties of the involved trace spaces including novel approximation properties. The source term in the streamfunction formulation is only a functional which prohibits its direct use in the DPG method. Therefore, we use recently developed regularization techniques. We prove optimal convergence rates for sufficiently smooth solutions. The built-in a posteriori error estimator of the DPG method can be used to steer adaptive refinements. Numerical experiments conclude the presentation.