数学
半群
类型(生物学)
数学分析
波动方程
柯西分布
柯西问题
误差分析
班级(哲学)
空格(标点符号)
应用数学
非线性系统
初值问题
物理
计算机科学
人工智能
操作系统
生物
量子力学
生态学
作者
Marlis Hochbruck,Bernhard Maier
出处
期刊:Ima Journal of Numerical Analysis
日期:2021-11-01
卷期号:42 (3): 1963-1990
被引量:7
标识
DOI:10.1093/imanum/drab073
摘要
Abstract In this paper we study space discretizations of a general class of first- and second-order quasilinear wave-type problems. We present a rigorous error analysis based on a combination of inverse estimates with semigroup theory for nonautonomous linear Cauchy problems. Moreover, we provide refined results for the special case that the nonlinearities are local in space. As applications of these general results we derive novel error estimates for two prominent examples from nonlinear physics: the Westervelt equation and the Maxwell equations with Kerr nonlinearity. We conclude with a numerical example to illustrate our theoretical findings.
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