ERROR ANALYSIS OF A FINITE ELEMENT METHOD FOR THE SPACE-FRACTIONAL PARABOLIC EQUATION Academic Article

abstract

• 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and H/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.

authors

• Lazarov, Raytcho
• Pasciak, Joseph

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Jin, B., Lazarov, R., Pasciak, J., & Zhou, Z.

citation count

• 77

complete list of authors

• Jin, Bangti||Lazarov, Raytcho||Pasciak, Joseph||Zhou, Zhi

publication date

• January 2014

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Error Estimate
• Finite Element Method
• Fully Discrete Scheme
• Semidiscrete Scheme
• Space Fractional Parabolic Equation

Digital Object Identifier (DOI)

• 10.1137/13093933X

URI

• https://hdl.handle.net/1969.1/183700

start page

• 2272

end page

• 2294

volume

• 52

issue

• 5

URL

• http%3A%2F%2Fdx.doi.org%2F10.1137%2F13093933x