@Article{IJNAM-20-6,
author = {Joseph, Fiordilino, Anthony and Winger, Matthew},
title = {Unconditionally Energy Stable and First-Order Accurate Numerical Schemes for the Heat Equation with Uncertain Temperature-Dependent Conductivity},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2023},
volume = {20},
number = {6},
pages = {805--831},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2023-1035},
url = {https://global-sci.com/article/82917/unconditionally-energy-stable-and-first-order-accurate-numerical-schemes-for-the-heat-equation-with-uncertain-temperature-dependent-conductivity}
}