Abstract
We present a Neumann-subproblem a posteriori finite element procedure for the efficient calculation of rigorous, constant-free, sharp lower and upper estimators for linear functional outputs of parabolic equations discretized by a discontinuous Galerkin method in time. We first formulate the bound procedure; we then provide illustrative numerical examples for problems of unsteady heat conduction.
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Machiels, L. (2000). Finite Element Output Bounds for Parabolic Equations: Application to Heat Conduction Problems. In: Cockburn, B., Karniadakis, G.E., Shu, CW. (eds) Discontinuous Galerkin Methods. Lecture Notes in Computational Science and Engineering, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59721-3_38
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DOI: https://doi.org/10.1007/978-3-642-59721-3_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64098-8
Online ISBN: 978-3-642-59721-3
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