Numerical Analysis of a Second order Pure Lagrange–Galerkin Method for Convection-Diffusion Problems. Part I: Time Discretization
Use este enlace para citar
http://hdl.handle.net/2183/35444Coleccións
- GI-M2NICA - Artigos [74]
Metadatos
Mostrar o rexistro completo do ítemTítulo
Numerical Analysis of a Second order Pure Lagrange–Galerkin Method for Convection-Diffusion Problems. Part I: Time DiscretizationData
2012-04-17Cita bibliográfica
Benítez, M., & Bermúdez, A. (2012). Numerical Analysis of a Second Order Pure Lagrange–Galerkin Method for Convection-Diffusion Problems. Part I: Time Discretization. SIAM Journal on Numerical Analysis, 50(2), 858-882. https://doi.org/10.1137/100809982
Resumo
[Abstract]: We propose and analyze a second order pure Lagrangian method for variable coefficient convection-(possibly degenerate) diffusion equations with mixed Dirichlet-Robin boundary conditions. First, the method is rigorously introduced for exact and approximate characteristics. Next, l1(H1) stability is proved and l1(H1) error estimates of order O(Δt2) are obtained. Moreover, l1(L2) stability and l1(L2) error estimates of order O(Δt2) with constants bounded in the hyperbolic limit are shown. For the particular case of Dirichlet boundary conditions, diffusion tensor A = ϵI and right-hand side f = 0, the l1(H1) stability estimate is independent of ϵ. Moreover, for incompressible flows the constants in the stability inequalities are independent of the final time. In a second part of this work, the pure Lagrangian scheme will be combined with Galerkin discretization using finite elements spaces and numerical examples will be presented.
Palabras chave
Convection-diffusion equation
Pure Lagrangian method
Characteristics method
Stability
Error estimates
Second order schemes
Pure Lagrangian method
Characteristics method
Stability
Error estimates
Second order schemes
Descrición
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/10.1137/100809982
Versión do editor
Dereitos
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)