Unconditionally Energy Stable and First-Order Accurate Numerical Schemes for the Heat Equation with Uncertain Temperature-Dependent Conductivity
Year: 2023
Author: Joseph Anthony Fiordilino, Matthew Winger
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 6 : pp. 805–831
Abstract
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving computational efficiency. Both mixed and Robin-type boundary conditions are treated. In contrast with alternative, related methodologies, stability and convergence are unconditional. In particular, we prove unconditional, energy stability and optimal-order error estimates. A battery of numerical tests are presented to illustrate both the theory and application of these algorithms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2023-1035
International Journal of Numerical Analysis and Modeling, Vol. 20 (2023), Iss. 6 : pp. 805–831
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Time-stepping finite element method heat equation temperature-dependent thermal conductivity uncertainty quantification.