Nathan V. Roberts

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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(More)
We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1, 2]. In our analysis, we develop an intrinsic a posteriori error indicator which we use for adaptive mesh generation. The DPG method is useful for the problem we consider because the method(More)
The discontinuous Petrov-Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan [15, 17] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. A key question that has not yet been answered in general—though there are some results for Poisson, e.g.—is how best to precondition the DPG(More)
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