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Zbl 1126.65081
Bermúdez, Alfredo; Nogueiras, Maria R.; Vázquez, Carlos
Numerical analysis of convection-diffusion-reaction problems with higher-order characteristics/finite elements. II: Fully discretized scheme and quadrature formulas. (English)
[J] SIAM J. Numer. Anal. 44, No. 5, 1854-1876 (2006). ISSN 0036-1429; ISSN 1095-7170/e

This paper deals with the higher-order Lagrange-Galerkin discretization method for a convection-reaction-diffusion equation with Dirichlet-Robin conditions at the boundary. Error estimates of order $O(\Delta t^2+h^k)$ are obtained and adequate quadrature formulas are proposed for the practical implementation of the method with particular finite element spaces. Numerical tests presented in the last part of the paper illustrate the theoretical results and the performance of the Lagrange-Galerkin schemes with quadrature formulas. [For part I see ibid. 44, No.~5, 1829--1853 (2006; Zbl 1126.65080), reviewed above.]
[Marius Ghergu (Dublin)]

MSC 2000:: *65M12 Stability and convergence of numerical methods (IVP of PDE)
65M25 Method of characteristics (numerical)
65M60 Finite numerical methods (IVP of PDE)
35K57 Reaction-diffusion equations
65M15 Error bounds (IVP of PDE)

Keywords: convection-diffusion-reaction equation; Lagrange-Galerkin methods; stability; second-order schemes; error estimates; quadrature formulas

Citations: Zbl 1126.65080

Cited in: Zbl 1126.65080

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