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A NEW MINIMIZATION PRINCIPLE FOR THE POISSON EQUATION LEADING TO A FLEXIBLE FINITE ELEMENT APPROACH
Part of:
Numerical approximation and computational geometry
Approximations and expansions
Numerical analysis: Ordinary differential equations
Published online by Cambridge University Press: 03 October 2017
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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2017 Australian Mathematical Society
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