arXiv (Cornell University)
Conforming and Nonconforming Finite Element Methods for Biharmonic Inverse Source Problem
June 2021 • Devika Shylaja, M. Thamban Nair
This paper deals with the numerical approximation of the biharmonic inverse source problem in an abstract setting in which the measurement data is finite-dimensional. This unified framework in particular covers the conforming and nonconforming finite element methods (FEMs). The inverse problem is analysed through the forward problem. Error estimate for the forward solution is derived in an abstract set-up that applies to conforming and Morley nonconforming FEMs. Since the inverse problem is ill-posed, Tikhonov reg…