Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems | Zendy

P. Lamichhane | Zendy

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Mixed Finite Element Methods for the Poisson Equation Using Biorthogonal and Quasi-Biorthogonal Systems

Author(s) -

P. Lamichhane

Publication year - 2013

Publication title -

advances in numerical analysis

Language(s) - English

Resource type - Journals

eISSN - 1687-9570

pISSN - 1687-9562

DOI - 10.1155/2013/189045

Subject(s) - biorthogonal system , lagrange multiplier , mathematics , finite element method , poisson's equation , mathematical analysis , a priori and a posteriori , mixed finite element method , finite field , mathematical optimization , discrete mathematics , physics , computer science , philosophy , wavelet transform , epistemology , artificial intelligence , wavelet , thermodynamics

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

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