ERROR ESTIMATES FOR A SEMIDISCRETE FINITE ELEMENT METHOD FOR FRACTIONAL ORDER PARABOLIC EQUATIONS Academic Article

abstract

• We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition (x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain . We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., H 2 () H 01 () and L 2 (). For the lumped mass method, the optimal L 2 -norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. 2013 Society for Industrial and Applied Mathematics.

authors

• Lazarov, Raytcho

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Jin, B., Lazarov, R., & Zhou, Z.

citation count

• 208

complete list of authors

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

publication date

• January 2013

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Finite Element Method
• Fractional Diffusion
• Lumped Mass Method
• Optimal Error Estimates
• Semidiscrete Gelerkin Method

Digital Object Identifier (DOI)

• 10.1137/120873984

start page

• 445

end page

• 466

volume

• 51

issue

• 1

URL

• http://dx.doi.org/10.1137/120873984