A <i>C</i>⁰ Nonconforming Virtual Element Method for the Kirchhoff Plate Obstacle Problem

Abstract

This paper investigates a novel C0 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 C0 nonconforming VEM, which originally lacked such degrees. This addition not only facilitates error estimation but also enhances its intuitiveness. Importantly, our novel C0 nonconforming VEM naturally satisfies the constraints of the obstacle problem. We then establish an a priori error estimate for our novel C0 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.

Keywords

• virtual element method
• fourth-order variational inequality
• plate obstacle problem
• a priori error estimate