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 the polygonal domain.
Morley Finite Element Method for the von K\'{a}rm\'{a}n Obstacle Problem
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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.
fields
math.NA 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
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 the polygonal domain.