Error bounds on semi-discrete finite element approximation of a moving-boundary system arising in concrete corrosion
Adrian Muntean 11 Centre for Analysis, Scientic computing and Applications (CASA), Department of Mathematics and Computer Science, Technical University of Eindhoven, PO Box 513, 5600 MB Eindhoven, The Netherlands.
Received by the editors June 30, 2006 and, in revised form May 17, 2007.
Finite element approximations of positive weak solutions to a one-phase unidimensional moving-boundary system with kinetic condition describing the penetration of a sharp-reaction interface in concrete are considered. A priori and a posteriori error estimates for the semi-discrete fields of active concentrations and for the position of the moving interface are obtained. The important feature of the system of partial differential equations is that the nonlinear coupling occurs due to the presence of both the moving boundary and the non-linearities of localized sinks and sources by reaction.
AMS subject classifications: 65M15, 65M60, 35R35
Key words: reaction-diffusion system; moving-boundary problem; spatial semi-discretization; finite elements; a priori estimates; a posteriori estimates; concrete corrosion