Constrained least-squares methods for partial differential equations

Conference paper (2006)
Faculty
Aerospace Engineering (Aerospace Engineering) (TU Delft)
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Published Date

08-09-2006

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Source:

ECCOMAS CFD 2006: Proceedings of the European Conference on Computational Fluid Dynamics, Egmond aan Zee, The Netherlands, September 5-8, 2006

Faculty

Aerospace Engineering

Abstract

Least-squares methods for partial differential equations are based on a norm-equivalence between the error norm and the residual norm. The resulting algebraic system of equations, which is symmetric positive definite, can also be obtained by solving a weighted collocation scheme using least-squares to solve the resulting algebraic equations. Furthermore, least-squares allows to ad extra constraints to the system. In the present work the entropy is added as an extra inequality constraint to ensure only physical solutions for the one-dimensional inviscid Burgers equation are obtained.