H1-second order convergent estimates for non-Fickian models

Authors:
S. Barbeiro;J. A. Ferreira;L. Pinto
Affiliations:
CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal;CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal;CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal
Venue:
Applied Numerical Mathematics
Year:
2011

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Abstract

In this paper we study numerical methods for integro-differential initial boundary value problems that arise, naturally, in many applications such as heat conduction in materials with memory, diffusion in polymers and diffusion in porous media. Here, we propose finite difference methods to compute approximations for the continuous solutions of such problems. We analyze stability and study convergence for those methods. Supraconvergent estimates are obtained. As such methods can be seen as lumped mass methods, our supraconvergent result corresponds to a superconvergent property in the context of finite element methods. Numerical results illustrating the theoretical results are included.