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∞(L2)-error estimates are derived under minimal smoothness assumptions on the initial data. Further, quasi-optimal estimates are shown to hold in L∞(L∞)-norm. Finally, the analysis is extended to the standard mixed method for HIDEs and optimal error estimates in L∞(L2)-norm are derived again under minimal smoothness on initial data.
Original language | English |
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Pages (from-to) | 113-134 |
Number of pages | 22 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 275 |
DOIs | |
Publication status | Published - Feb 2015 |
Keywords
- Completely discrete implicit method
- Hyperbolic integro-differential equation
- Minimal smoothness on initial data
- Mixed finite element method
- Optimal error estimates
- Semidiscrete Galerkin approximation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics