A Posteriori Error Estimates for the Crank–Nicolson Method: Application to Parabolic Partial Differential Equations Subject to a Robin Boundary Condition with Small Randomness

• Published in: Journal of scientific computing Vol. 104; no. 1; p. 7
• Main Authors: Shravani, N., Reddy, G. M. M., Vynnycky, M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2025; Springer Nature B.V
• Subjects: Algorithms; Boundary conditions; Computational Mathematics and Numerical Analysis; Crank-Nicholson method; Estimates; Expected values; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical functions; Mathematics; Mathematics and Statistics; Numerical analysis; Parabolic differential equations; Parameter uncertainty; Partial differential equations; Perturbation methods; Power series; Random variables; Theoretical; Finite element method; 65M15; Perturbation technique; error analysis; Small random input data; Parabolic PDE; 65M60; Crank–Nicolson scheme

In this article, we obtain residual-based a posteriori error estimates for a linear parabolic partial differential equation which is subject to a Robin boundary condition that contains a small uncertainty. To this end, the perturbation technique is exploited to express the exact random solution in t...