Convergence analysis for a class of high-order semi-Lagrangian advection schemes

被引:120
作者
Falcone, M
Ferretti, R
机构
[1] Univ Rome La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy
关键词
hyperbolic equations; method of characteristics; semi-Lagrangian schemes; high-order schemes; convergence; stability;
D O I
10.1137/S0036142994273513
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The convergence properties of a class of high-order semi-Lagrangian schemes for pure advection equations are studied here in the framework of the theory of viscosity solutions. We review the general convergence results for discrete-time approximation schemes belonging to that class and we prove some a priori estimates in L-infinity and L-2 for the rate of convergence of fully discrete schemes. We prove then that a careful coupling of time and space discretizations can allow large time steps in the numerical integration still preserving the accuracy of the solutions. Several examples of schemes and numerical tests are presented.
引用
收藏
页码:909 / 940
页数:32
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