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This paper derives a higher order hybrid stress finite element method on quadrilateral meshes for linear plane elasticity problems. The method employs continuous piecewise bi-quadratic functions in local coordinates to approximate the displacement vector and a piecewise-independent 15-parameter mode to approximate the stress tensor. Error estimation shows that the method is free from Poisson-locking and has second-order accuracy in the energy norm. Numerical experiments confirm the theoretical results.

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

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Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

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Uniform Convergence Analysis of a Higher Order Hybrid Stress Quadrilateral Finite Element Method for Linear Elasticity Problems

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process