Observatorio de I+D+i UPM

Memorias de investigación
Research Publications in journals:
MODIFIED LAGRANGE-GALERKIN METHODS OF FIRST AND SECOND ORDER IN TIME FOR CONVECTIONDIFFUSION PROBLEMS
Year:2012
Research Areas
  • Mathematics
Information
Abstract
We introduce modified Lagrange?Galerkin (MLG) methods of order one and two with respect to time to integrate convection?diffusion equations. As numerical tests show, the new methods are more efficient, but maintaining the same order of convergence, than the conventional Lagrange?Galerkin (LG) methods when they are used with either P 1 or P 2 finite elements. The error analysis reveals that: (1) when the problem is diffusion dominated the convergence of the modified LG methods is of the form O(h m+1 + h 2 + ?t q ), q = 1 or 2 and m being the degree of the polynomials of the finite elements; (2) when the problem is convection dominated and the time step ?t is large enough the convergence is of the form O(hm+1?t+h2+?tq) ; (3) as in case (2) but with ?t small, then the order of convergence is now O(h m + h 2 + ?t q ); (4) when the problem is convection dominated the convergence is uniform with respect to the diffusion parameter ? (x, t), so that when ? ? 0 and the forcing term is also equal to zero the error tends to that of the pure convection problem. Our error analysis shows that the conventional LG methods exhibit the same error behavior as the MLG methods but without the term h 2. Numerical experiments support these theoretical results.
International
Si
JCR
Si
Title
Numerische Mathematik
ISBN
0029-599X
Impact factor JCR
1,388
Impact info
Datos JCR del año 2010
Volume
Journal number
From page
601
To page
638
Month
ABRIL
Ranking
Participants
  • Autor: Laura Saavedra Lago (UPM)
  • Autor: Rodolfo Bermejo Bermejo (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Análisis y experimentación en mecánica de fluidos y combustión
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)