Convergence analysis of a discontinuous Galerkin method for a sub-diffusion equation

Numerical Algorithms

Volumn 52, Issue 1, 2009, Pages 69-88

  McLean, William ^a   Mustapha, Kassem ^b  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Finite elements; Memory term; Non uniform time steps

Indexed keywords

EID: 70350618343     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-008-9258-8     Document Type: Article

References (10)

1. Cuesta, E., Lubich, C., Palencia, C.: Convolution quadrature time discretization of fractional diffusive-wave equations. Math. Comput. 75, 673-696 (2006).
2. Langlands, T.A.M., Henry, B.I.: The accuracy and stability of an implicit solution method for the fractional diffusion equation. J. Comp. Phys. 205, 719-936 (2005).
3. López-Fernández, M., Lubich, C., Schädle, A.: Adaptive, fast and oblivious convolution quadrature in evolution equations with memory. SIAM J. Sci. Comput. 30, 1015-1037 (2008).
4. López-Fernandez, M., Palencia, C., Schädle, A.: A spectral order method for inverting sectorial Laplace transforms. SIAM J. Numer. Anal. 44, 1332-1350 (2006).
5. Metzler, R., Klafter, J.: The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 339, 1-77 (2000).
6. McLean, W., Thomée, V.: Numerical solution via Laplace transforms of a fractional order evolution equation. J. Integral Equ. Appl. (2008, in press).
7. McLean, W., Thomée, V.: Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional order evolution equation. IMA J. Numer. Anal. (2008, in press).
8. McLean, W., Thomée, V., Wahlbin, L.B.: Discretization with variable time steps of an evolution equation with a positive-type memory term. J. Comput. Appl. Math. 69, 49-69 (1996).
9. Mustapha, K., McLean, W.: Discontinuous Galerkin method for an evolution equation with a memory term of positive type. Math. Comput. (2008, in press).
10. Schädle, A., López-Fernandez, M., Lubich, C.: Fast and oblivious convolution quadrature. SIAM J. Sci. Comput. 28, 421-438 (2006).