We introduce two three-field mixed formulations for the Poisson equation and propose finite element methods for their approximation. Both mixed formulations are obtained by introducing a weak equation for the gradient of the solution by means of a Lagrange multiplier space. Two efficient numerical schemes are proposed based on using a pair of bases for the gradient of the solution and the Lagrange multiplier space forming biorthogonal and quasi-biorthogonal systems, respectively. We also establish an optimal a priori error estimate for both finite element approximations.
CITATION STYLE
Lamichhane, B. P. (2013). Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems. Advances in Numerical Analysis, 2013, 1–9. https://doi.org/10.1155/2013/189045
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