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arXiv · 2309.05303

Morley Type Virtual Element Method for Von K\'{a}rm\'{a}n Equations

Devika Shylaja·Sarvesh Kumar
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Abstract

This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n 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.

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Devika Shylaja, Sarvesh Kumar. 2023-09-11. Morley Type Virtual Element Method for Von K\'{a}rm\'{a}n Equations. https://arxiv.org/abs/2309.05303

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