Numerical Analysis of a Second Order Pure Lagrange--Galerkin Method for Convection-Diffusion Problems. Part II: Fully Discretized Scheme and Numerical Results
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Numerical Analysis of a Second Order Pure Lagrange--Galerkin Method for Convection-Diffusion Problems. Part II: Fully Discretized Scheme and Numerical ResultsFecha
2012-11-01Cita bibliográfica
Benitez, M., & Bermudez, A. (2012). Numerical Analysis of a Second Order Pure Lagrange--Galerkin Method for Convection-Diffusion Problems. Part II: Fully Discretized Scheme and Numerical Results. SIAM Journal on Numerical Analysis, 50(6), 2824-2844. https://doi.org/10.1137/100809994
Resumen
[Abstract]: We analyze a second order pure Lagrange-Galerkin method for variable coefficient
convection-(possibly degenerate) diffusion equations with mixed Dirichlet-Robin boundary conditions.
In a previous paper the proposed second order pure Lagrangian time discretization scheme
has been introduced and analyzed for the same problem. More precisely, the l1(H1) stability and
l1(H1) error estimates of order O(_t2) has been obtained. Moreover, for the particular case of
incompressible flows, stability inequalities with constants independent of the final time have been
stated. In the present paper l1(H1) error estimates of order O(_t2) + O(hk) are obtained for the
fully discretized pure Lagrange-Galerkin method. To prove these results we use some properties
obtained in the previous paper. Finally, numerical tests are presented that confirm the theoretical
results.
Palabras clave
Convection-diffusion equation
Lagrangian method
Characteristics method
Galerkin discretization
Stability
Error estimates
Second order schemes
Lagrangian method
Characteristics method
Galerkin discretization
Stability
Error estimates
Second order schemes
Descripción
This version of the article has been accepted for publication, after peer
review, but is not the Version of Record and does not reflect post-acceptance
improvements, or any corrections. The Version of Record is available online
at: https://doi.org/10.1137/100809994
Versión del editor
Derechos
This manuscript version is made available under the CC-BY 4.0 International
license
https://creativecommons.org/licenses/by/4.0/
ISSN
0036-1429
1095-7170 (e-ISSN)
1095-7170 (e-ISSN)