Error Estimates and Superconvergence of a High-Accuracy Difference Scheme for a Parabolic Inverse Problem with Unknown Boundary Conditions
Liping Zhou ,
Shi Shu and
Haiyuan Yu
10.4208/nmtma.OA-2018-0019
Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1119-1140.
In this work, we firstly construct an implicit Euler difference scheme for a one-dimensional parabolic inverse problem with a unknown time-dependent function in the boundary conditions. Then we initially prove that this scheme can reach the asymptotic optimal error estimate in the maximum norm. Next, we present some approximation formulas for the solution derivative and the unknown boundary function and prove that they have superconvergence properties. In the end, numerical experiment demonstrates the theoretical results.
