Morley type virtual element method for von Kármán equations

This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von Kármán equations  that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise \(H^1\) $H^1$ and \(L^2\) $L^2$ norms are also derived. A working procedure to find an approximation for the discrete solution using Newton’s method is discussed. Numerical results that justify theoretical estimates are presented.