Some new error estimates of a semidiscrete finite volume element method for a parabolic integro-differential equation with nonsmooth initial data Academic Article

abstract

• A semidiscrete finite volume element (FVE) approximation to a parabolic integro-differential equation (PIDE) is analyzed in a two-dimensional convex polygonal domain. An optimal-order L 2-error estimate for smooth initial data and nearly the same optimal-order L 2-error estimate for nonsmooth initial data are obtained. More precisely, for homogeneous equations, an elementary energy technique and a duality argument are used to derive an error estimate of order O (t -1/h 2 ln h) in the L 2-norm for positive time when the given initial function is only in L 2. 2006 Society for Industrial and Applied Mathematics.

authors

• Lazarov, Raytcho

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Sinha, R. K., Ewing, R. E., & Lazarov, R. D.

citation count

• 25

complete list of authors

• Sinha, RK||Ewing, RE||Lazarov, RD

publication date

• January 2006

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Integro-differential Equation
• Optimal-order Error Estimate
• Parabolic Equation
• Smooth And Nonsmooth Initial Data

Digital Object Identifier (DOI)

• 10.1137/040612099

start page

• 2320

end page

• 2343

volume

• 43

issue

• 6

URL

• http://dx.doi.org/10.1137/040612099