Morley Type Virtual Element Method for Von Kármán Equations

2023/09/11 by Devika Shylaja, Shylaja, Devika, Sarvesh Kumar +1
Engineering · Mathematics · #35J61 #65N12 #65N30 #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2309.05303

openalex publication_date 2023/09/11 · openalex created_date 2023/09/13 · openalex updated_date 2026/07/28

Abstract

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 H¹ and L² 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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