Morley Type Virtual Element Method for Von Kármán Equations

09/11/2023

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by   Devika Shylaja, et al.

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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 and L^2 norm are also derived. A working procedure to find an approximation for the discrete solution using Newtons method is discussed. Numerical results that justify theoretical estimates are presented.