Browsing by Author "Gopalakrishnan, Jayadeep"
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Item Analysis of the DPG method for the Poisson equation(University of Minnesota. Institute for Mathematics and Its Applications, 2010-10) Demkowicz, L.; Gopalakrishnan, JayadeepItem An analysis of the practical DPG method(University of Minnesota. Institute for Mathematics and Its Applications, 2011-07) Gopalakrishnan, Jayadeep; Qiu, W.Item A characterization of hybridized mixed methods for second order elliptic problems(2002-11) Cockburn, Bernardo; Gopalakrishnan, JayadeepIn this paper, we give a new characterization of the approximate solution given by hybridized mixed methods for second-order, self-adjoint elliptic problems. We apply this characterization to obtain an explicit formula for the entries of the matrix equation for the Lagrange multiplier unknowns resulting from hybridization. We also obtain necessary and sufficient conditions under which the multipliers of the Raviart-Thomas and the Brezzi-Douglas-Marini methods of similar order are identical.Item Commuting smoothed projectors in weighted norms with an application to axisymmetric Maxwell equations(University of Minnesota. Institute for Mathematics and Its Applications, 2011-01) Gopalakrishnan, Jayadeep; Oh, M.Item Locking-free hp DGP method for linear elasticity with symmetric stresses(University of Minnesota. Institute for Mathematics and Its Applications, 2011-05) Bramwell, J.; Demkowicz, L.; Gopalakrishnan, Jayadeep; Qiu, W.Item Mortar estimates independent of number of subdomains(1999-12) Gopalakrishnan, JayadeepItem A multilevel discontinuous Galerkin method(2000-12) Gopalakrishnan, Jayadeep; Kanschat, GuidoA variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate is proved. A multigrid algorithm for this method is presented, and numerical experiments indicating its robustness with respect to diffusion coefficient are reported.Item Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations(2000-06) Gopalakrishnan, Jayadeep; Pasciak, Joseph E.Item Partial expansion of a Lipschitz domain and some applications(University of Minnesota. Institute for Mathematics and Its Applications, 2011-02) Gopalakrishnan, Jayadeep; Qiu, W.