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Title: Adaptivity and blow-up detection for nonlinear evolution problems
Authors: Cangiani, Andrea
Georgoulis, Emmanuil H.
Kyza, Irene
Metcalfe, Stephen
First Published: 20-Dec-2016
Citation: SIAM Journal on Scientific Computing, 2016, 38 (6), pp. A3833-A3856
Abstract: This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically, a posteriori error bounds are derived in the $L^{\infty}(L^2)+L^2(H^1)$-type norm for a first order in time implicit-explicit interior penalty discontinuous Galerkin in space discretization of the problem, although the theory presented is directly applicable to the case of conforming finite element approximations in space. The choice of the discretization in time is made based on a careful analysis of adaptive time-stepping methods for ODEs that exhibit finite time blow-up. The new adaptive algorithm is shown to accurately estimate the blow-up time of a number of problems, including one which exhibits regional blow-up.
DOI Link: 10.1137/16M106073X
ISSN: 1064-8275
eISSN: 1095-7197
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2016 Society for Industrial and Applied Mathematics. Deposited with reference to the publisher’s open access archiving policy.
Appears in Collections:Published Articles, Dept. of Mathematics

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