Optimal error estimates of mixed FEMs for second order hyperbolic\n integro-differential equations with minimal smoothness on initial data

2014/01/20 by Samir Karaa, Karaa, Samir, Amiya K. Pani +1
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Applied mathematics #Differential equation #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #First order #Hyperbolic partial differential equation #Mathematical analysis #Mathematics #Norm (philosophy) #Numerical Analysis (math.NA) #Numerical methods for differential equations #Numerical methods in engineering #Smoothness

paper · pdf · doi:10.48550/arxiv.1401.5134

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2014/01/20 · openalex created_date 2022/10/04 · openalex updated_date 2026/08/01

Abstract

In this article, mixed finite element methods are discussed for a class of\nhyperbolic integro-differential equations (HIDEs). Based on a modification of\nthe nonstandard energy formulation of Baker, both semidiscrete and completely\ndiscrete implicit schemes for an extended mixed method are analyzed and optimal\nL^\∞(L²)-error estimates are derived under minimal smoothness\nassumptions on the initial data. Further, quasi-optimal estimates are shown to\nhold in L^\∞(L^\∞)-norm. Finally, the analysis is extended to the\nstandard mixed method for HIDEs and optimal error estimates in\nL^\∞(L²)-norm are derived again under minimal smoothness on initial\ndata.\n

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