TY - JOUR
T1 - Unconditionally Energy Stable and First-Order Accurate Numerical Schemes for the Heat Equation with Uncertain Temperature-Dependent Conductivity
AU - Fiordilino , Joseph Anthony
AU - Winger , Matthew
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 805
EP - 831
PY - 2023
DA - 2023/11
SN - 20
DO - http://doi.org/10.4208/ijnam2023-1035
UR - https://global-sci.org/intro/article_detail/ijnam/22142.html
KW - Time-stepping, finite element method, heat equation, temperature-dependent thermal conductivity, uncertainty quantification.
AB - <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>