In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariat...In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.展开更多
Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive r...Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms.An adaptive strategy based on theℜ-parameter is proposed for continuous flows,while a hybrid adaptive algorithm employing a combination of error indicators and theℜ-parameter is developed for discontinuous flows.Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.展开更多
文摘In this paper, we establish the stochastic ordering of median from an exchangeable trivaxiate normal vector based on the strength of the correlation coefficient. Specifically, by considering two exchangeable trivariate normal vectors with different correlation coefficients, we show that the absolute value of the median in the vector with smaller correlation coefficient is stochastically smaller than the absolute value of the median in the vector with larger correlation coefficient. We prove this result by utilizing skew-normal distributions.
文摘Algorithms for adaptive mesh refinement using a residual error estimator are proposed for fluid flow problems in a finite volume framework.The residual error estimator,referred to as theℜ-parameter is used to derive refinement and coarsening criteria for the adaptive algorithms.An adaptive strategy based on theℜ-parameter is proposed for continuous flows,while a hybrid adaptive algorithm employing a combination of error indicators and theℜ-parameter is developed for discontinuous flows.Numerical experiments for inviscid and viscous flows on different grid topologies demonstrate the effectiveness of the proposed algorithms on arbitrary polygonal grids.
