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An a priori error estimate for a monotone mixed finite-element discretization of a convection–diffusion problem

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Abstract

We present a local exponential fitting hybridized mixed finite-element method for convection–diffusion problem on a bounded domain with mixed Dirichlet Neuman boundary conditions. With a new technique that interpretes the algebraic system after static condensation as a bilinear form acting on certain lifting operators we prove an a priori error estimate on the Lagrange multipliers that requires minimal regularity. While an extension of more classical arguments provide an estimate for the other solution components.

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  1. Institut für Mathematik, Johannes Gutenberg-Universität Mainz, Staudinger Weg 9, Mainz, Germany

    Stefan Holst

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  1. Stefan Holst
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Holst, S. An a priori error estimate for a monotone mixed finite-element discretization of a convection–diffusion problem. Numer. Math. 109, 101–119 (2008). https://doi.org/10.1007/s00211-007-0097-7

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  • DOI: https://doi.org/10.1007/s00211-007-0097-7

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