Error analysis of implicit Euler methods for quasilinear hyperbolic evolution equations

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• 作者：Marlis Hochbruck ; Tomislav Pažur
• 关键词：Mathematics Subject ClassificationPrimary 65M12 ; 65J15 ; Secondary 35Q61 ; 35L90
• 刊名：Numerische Mathematik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：135
• 期：2
• 页码：547-569
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Numerical Analysis; Mathematics, general; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation; Appl.Mathematics/Comput
• 出版者：Springer Berlin Heidelberg
• ISSN：0945-3245
• 卷排序：135

文摘

In this paper we study the convergence of the semi-implicit and the implicit Euler methods for the time integration of abstract, quasilinear hyperbolic evolution equations. The analytical framework considered here includes certain quasilinear Maxwell’s and wave equations as special cases. Our analysis shows that the Euler approximations are well-posed and convergent of order one. The techniques will be the basis for the future investigation of higher order time integration methods and full discretizations of certain quasilinear hyperbolic problems.