Preserving positivity for hyperbolic PDEs using variable-order finite elements with bounded polynomials

Authors:
M. Berzins
Affiliations:
SCI Institute, School of Computing, University of Utah, Salt Lake City, UT 84112-9205, USA
Venue:
Applied Numerical Mathematics - Adaptive methods for partial differential equations and large-scale computation
Year:
2005

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Abstract

The positivity preserving approach of Berzins is generalized by using a derivation based on bounded polynomial approximations and order selection. The approach is extended from the B-spline based methods used previously to the use of more conventional continuous Galerkin elements. The conditions relating to positivity preservation are considered and a numerical example used to demonstrate the performance of the method on a model advection equation problem.