A C 0 Nonconforming Virtual Element Method for the Kirchhoff Plate Obstacle Problem.

This paper investigates a novel C 0 nonconforming virtual element method (VEM) for solving the Kirchhoff plate obstacle problem, which is described by a fourth-order variational inequality (VI) of the first kind. In our study, we distinguish our approach by introducing new internal degrees of freedom to the traditional lowest-order C 0 nonconforming VEM, which originally lacked such degrees. This addition not only facilitates error estimation but also enhances its intuitiveness. Importantly, our novel C 0 nonconforming VEM naturally satisfies the constraints of the obstacle problem. We then establish an a priori error estimate for our novel C 0 nonconforming VEM, with the result indicating that the lowest order of our method achieves optimal convergence. Finally, we present a numerical example to validate the theoretical result. [ABSTRACT FROM AUTHOR]