Optimal error estimates of mixed FEMs for second order hyperbolic integro-differential equations with minimal smoothness on initial data
Numerical Analysis
2014-01-22 v1
Abstract
In this article, mixed finite element methods are discussed for a class of hyperbolic integro-differential equations (HIDEs). Based on a modification of the nonstandard energy formulation of Baker, both semidiscrete and completely discrete implicit schemes for an extended mixed method are analyzed and optimal L^{\infty}(L^2)-error estimates are derived under minimal smoothness assumptions on the initial data. Further, quasi-optimal estimates are shown to hold in L^{\infty}(L^{\infty})-norm. Finally, the analysis is extended to the standard mixed method for HIDEs and optimal error estimates in L^{\infty}(L^2)-norm are derived again under minimal smoothness on initial data.
Cite
@article{arxiv.1401.5134,
title = {Optimal error estimates of mixed FEMs for second order hyperbolic integro-differential equations with minimal smoothness on initial data},
author = {Samir Karaa and Amiya K. Pani},
journal= {arXiv preprint arXiv:1401.5134},
year = {2014}
}