A LIMITING STRATEGY FOR THE BACK AND FORTH ERROR COMPENSATION AND CORRECTION METHOD FOR SOLVING ADVECTION EQUATIONS

作     者：Hu, Lili Li, Yao Liu, Yingjie 

作者机构：Georgia Inst Technol Sch Math Atlanta GA 30332 USA NYU Courant Inst Math New York NY USA 

出 版 物：《MATHEMATICS OF COMPUTATION》 (计算数学)

年 卷 期：2016年第85卷第299期

页      面：1263-1280页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：NSF [DMS-1115671] 

主　　题：ADVECTION MATHEMATICAL models HAMILTON-Jacobi equations INTERPOLATION algorithms DERIVATIVES (Mathematics) PARTIAL differential equations 

摘      要：We further study the properties of the back and forth error compensation and correction (BFECC) method for advection equations such as those related to the level set method and for solving Hamilton-Jacobi equations on unstructured meshes. In particular, we develop a new limiting strategy which requires another backward advection in time so that overshoots/undershoots on the new time level get exposed when they are transformed back to compare with the solution on the old time level. This new technique is very simple to implement even for unstructured meshes and is able to eliminate artifacts induced by jump discontinuities in derivatives of the solution as well as by jump discontinuities in the solution itself (even if the solution has large gradients in the vicinities of a jump). Typically, a formal second order method for solving a time dependent Hamilton-Jacobi equation requires quadratic interpolation in space. A BFECC method on the other hand only requires linear interpolation in each step, thus is local and easy to implement even for unstructured meshes.