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Zbl 0914.65097
Falcone, Maurizio; Ferretti, Roberto
Convergence analysis for a class of high-order semi-Lagrangian advection schemes. (English)
[J] SIAM J. Numer. Anal. 35, No.3, 909-940 (1998). ISSN 0036-1429; ISSN 1095-7170/e

Following model problems are discussed: $$v(x,t)_t=\lambda v(x,t)+f(x)\cdot\nabla v(x,t)+g(x);\quad v(x,0)=v_0(x)$$ $$\lambda v(x,t)+ f(x)\cdot \nabla v(x,t)+ g(x)=0.$$ The authors examine a class of semi-Lagrangian approximation schemes. In these methods the approximate solution is computed along a grid approximating the characteristics. The main results concern a priori estimates in $L^\infty$ and $L^2$ as well as the rate of convergence of the fully discrete scheme. By coupling time and space discretizations large time steps can be used without damaging the accuracy of the solutions. Results are illustrated by several numerical tests.
[E.Schechter (Kaiserslautern)]

MSC 2000:: *65M25 Method of characteristics (numerical)
35L45 First order hyperbolic systems, initial value problems
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: hyperbolic equations; method of characteristics; semi-Lagrangian schemes; high-order schemes; convergence; stability; numerical tests

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