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A NEW MINIMIZATION PRINCIPLE FOR THE POISSON EQUATION LEADING TO A FLEXIBLE FINITE ELEMENT APPROACH

Part of: Numerical analysis: Ordinary differential equations Numerical approximation and computational geometry Approximations and expansions

Published online by Cambridge University Press:  03 October 2017

B. P. LAMICHHANE Open the ORCID record for B. P. LAMICHHANE [Opens in a new window]
B. P. LAMICHHANE*
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia email Bishnu.Lamichhane@newcastle.edu.au
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Abstract

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A new minimization principle for the Poisson equation using two variables – the solution and the gradient of the solution – is introduced. This principle allows us to use any conforming finite element spaces for both variables, where the finite element spaces do not need to satisfy the so-called inf–sup condition. A numerical example demonstrates the superiority of this approach.

Keywords

Poisson equationminimization principlemixed finite element methoda priori error estimate

MSC classification

Primary: 65D15: Algorithms for functional approximation
Secondary: 65L60: Finite elements, Rayleigh-Ritz, Galerkin and collocation methods 41A15: Spline approximation
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 232 - 239
Copyright
© 2017 Australian Mathematical Society 

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