Finite Element Methods with Numerical Quadrature for Parabolic Integrodifferential Equations

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise-linear finite element methods for parabolic integrodifferential equations. We give error estimates for both smooth and nonsmooth initial data. Our results generalize those obtained for the lumped mass m...

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Bibliographic Details
Published inSIAM journal on numerical analysis Vol. 33; no. 3; pp. 1084 - 1105
Main Authors Pani, Amiya K., Peterson, Todd E.
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.1996
Subjects
A priori knowledge
Approximation
Bribery
Differential equations
Error rates
Estimates
Estimation methods
Exact sciences and technology
Finite element method
Inequality
Integral equations, integral transforms
Mathematics
Methods
Numerical analysis
Numerical analysis. Scientific computation
Numerical quadratures
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Preliminary estimates
Sciences and techniques of general use
Error estimation
Initial value problem
Partial differential equation
Finite element method
Quadrature
Parabolic equation
Numerical analysis
Boundary value problem
Integral equation
Quadrature formula
Integrodifferential equation
Integral transformation
Finite element
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Summary:We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise-linear finite element methods for parabolic integrodifferential equations. We give error estimates for both smooth and nonsmooth initial data. Our results generalize those obtained for the lumped mass method.
ISSN:0036-1429
1095-7170
DOI:10.1137/0733053