Stability and convergence of fully discrete finite element schemes for the acoustic wave equation

Samir Karaa*

*المؤلف المقابل لهذا العمل

نتاج البحث: المساهمة في مجلةمراجعة النظراء

10 اقتباسات (Scopus)

ملخص

In this paper, we investigate the stability and convergence of some fully discrete finite element schemes for solving the acoustic wave equation where a discontinuous Galerkin discretization in space is used. We first review and compare conventional time-stepping methods for solving the acoustic wave equation. We identify their main properties and investigate their relationship. The study includes the Newmark algorithm which has been used extensively in applications. We present a rigorous stability analysis based on the energy method and derive sharp stability results covering some well-known CFL conditions. A convergence analysis is carried out and optimal a priori error estimates are obtained. For sufficiently smooth solutions, we demonstrate that the maximal error in the L2-norm error over a finite time interval converges optimally as O(hp+1+Δts ), where p denotes the polynomial degree, s=1 or 2, h the mesh size, and Δt the time step.

اللغة الأصليةEnglish
الصفحات (من إلى)659-682
عدد الصفحات24
دوريةJournal of Applied Mathematics and Computing
مستوى الصوت40
رقم الإصدار1-2
المعرِّفات الرقمية للأشياء
حالة النشرPublished - أكتوبر 2012

ASJC Scopus subject areas

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بصمة

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