University Digital Conservancy :: Browsing by Author "Cockburn, Bernardo"

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An a priori error analysis of the local discontinuous Galerkin method for elliptic problems

(2000-04) Castillo, Paul; Cockburn, Bernardo; Perugia, Ilaria; Schotzau, Dominik

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An adaptive method with rigorous error control for the Hamilton-Jacobi equations. Part II: The two-dimensional steady state case

(2004-09) Cockburn, Bernardo; Yenikaya, Bayram

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An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems

(2006-11) Cockburn, Bernardo; Dong, Bo

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A characterization of hybridized mixed methods for second order elliptic problems

(2002-11) Cockburn, Bernardo; Gopalakrishnan, Jayadeep

In 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.

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Continuous dependence and error estimation for viscosity methods

(2003-04) Cockburn, Bernardo

In this paper, we review some ideas on continuous dependence results for the entropy solution of hyperbolic scalar conservation laws. They lead to a complete L (L1)-approximation theory with which error estimates for numerical methods for this type of equations can be obtained. The approach we consider consists in obtaining continuous dependence results for the solutions of parabolic conservation laws and deducing from them the corresponding results for the entropy solution. This is a natural approach as the entropy solution is nothing but the limit of solutions of parabolic scalar conservation laws as the viscosity coefficient goes to zero.