INVESTIGADORES
STORTI Mario Alberto
artículos
Título:
A Petrov-Galerkin formulation for advection-reaction-diffusion
Autor/es:
IDELSOHN, SERGIO; NIGRO NORBERTO; STORTI MARIO; BUSCAGLIA, GUSTAVO
Revista:
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Editorial:
Elsevier
Referencias:
Lugar: Amsterdam, Holanda; Año: 1997 vol. 136 p. 27 - 46
ISSN:
0045-7825
Resumen:
In this work we present a new method called (SU + C)PG to solve
advection-reaction-diffusion scalar equations by the Finite Element
Method (FEM). The SUPG (for Streamline Upwind Petrov-Galerkin)
method is currently one of the most popular methods for
advection-diffusion problems due to its inherent consistency and
efficiency in avoiding the spurious oscillations obtained from the
plain Galerkin method when there are discontinuities in the solution.
Following this ideas, Tezduyar and Park treated the more general
advection-reaction-diffusion problem and they developed a stabilizing
term for advection-reaction problems without significant diffusive
boundary layers. In this work an SUPG extension for all situations is
performed, covering the whole plane represented by the Peclet number
and the dimensionless reaction number. The scheme is based on the
extension of the super-convergence feature through the inclusion of an
additional perturbation function and a corresponding proportionality
constant. Both proportionality constants (that one corresponding to the
standard perturbation function from SUPG, and the new one introduced
here) are selected in order to verify the super-convergence feature,
i.e. exact nodal values are obtained for a restricted class of problems
(uniform mesh, no source term, constant physical properties). It is
also shown that the (SU + C)PG scheme verifies the Discrete Maximum
Principle (DMP), that guarantees uniform convergence of the finite
element solution. Moreover, it is shown that super-convergence is
closely related to the DMP, motivating the interest in developing
numerical schemes that extend the super-convergence feature to a
broader class of problems.