Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Error estimates for semidiscrete finite element methods for parabolic integro-differential equations


Authors: Vidar Thomée and Nai Ying Zhang
Journal: Math. Comp. 53 (1989), 121-139
MSC: Primary 65R20; Secondary 65M60
MathSciNet review: 969493
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is to attempt to carry over known results for spatially discrete finite element methods for linear parabolic equations to integro-differential equations of parabolic type with an integral kernel consisting of a partial differential operator of order $ \beta \leq 2$. It is shown first that this is possible without restrictions when the exact solution is smooth. In the case of a homogeneous equation with nonsmooth initial data $ v,v \in {L_2}$, optimal $ O({h^r})$ convergence for positive time is possible in general only if $ r \leq 4 - \beta $. This depends on the fact that the exact solution is then only in $ {H^{4 - \beta }}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65R20, 65M60

Retrieve articles in all journals with MSC: 65R20, 65M60


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1989-0969493-9
PII: S 0025-5718(1989)0969493-9
Keywords: Integro-differential equation, parabolic, nonsmooth data, regularity estimates, finite elements, Galerkin, semidiscrete, error estimates
Article copyright: © Copyright 1989 American Mathematical Society