Approximation of Viscous Transport and Conservative Equations with One Sided Lipschitz Velocity Fields

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2026-06-23 DOI:10.1137/25m1760350

Fabio Camilli, Adriano Festa, Luciano Marzufero

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 64, Issue 3, Page 1043-1071, June 2026.
Abstract. The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the convergence of the schemes, we exploit the characterization of the solution for these equations expressed in terms of measurable time-dependent viscosity solution and, respectively, duality solution. We supplement our theoretical analysis with various numerical examples to illustrate the features of the schemes.

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单侧Lipschitz速度场的粘性输运和保守方程的近似

SIAM数值分析杂志，64卷，第3期，1043-1071页，2026年6月。摘要。本文的目的是研究满足单侧Lipschitz条件的具有可测量系数的粘性输运和保守方程在非结构网格上的半拉格朗日近似格式。为了建立这些格式的收敛性，我们利用了这些方程的解的特征，分别用可测量的随时间变化的粘度解和对偶解表示。在理论分析的基础上，我们用各种数值例子来说明这些方案的特点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.