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Morley Finite Element Method for the von K\'{a}rm\'{a}n Obstacle Problem
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This paper focusses on the von K\'{a}rm\'{a}n equations for the moderately large deformation of a very thin plate with the convex obstacle constraint leading to a coupled system of semilinear fourth-order obstacle problem and motivates its nonconforming Morley finite element approximation. The first part establishes the well-posedness of the von K\'{a}rm\'{a}n obstacle problem and also discusses the uniqueness of the solution under an a priori and an a posteriori smallness condition on the data. The second part of the article discusses the regularity result of Frehse from 1971 and combines it with the regularity of the solution on a polygonal domain. The third part of the article shows an a priori error estimate for optimal convergence rates for the Morley finite element approximation to the von K\'{a}rm\'{a}n obstacle problem for small data. The article concludes with numerical results that illustrates the requirement of smallness assumption on the data for optimal convergence rate.
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Cited by 1 Pith paper
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A Quadratic $C^0$ Interior Penalty Method for the von K\'{a}rm\'{a}n Obstacle Problem
A quadratic C0 interior penalty method for the von Kármán obstacle problem is proved to have discrete solutions converging in the discrete energy norm with order O(h^α), where α is the biharmonic regularity index of t...
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