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Unconditionally Energy Stable and First-Order Accurate Numerical Schemes for the Heat Equation with Uncertain Temperature-Dependent Conductivity

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.

Author Details

Joseph Anthony Fiordilino

Matthew Winger

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