In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite...In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]展开更多
The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian ...The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method.展开更多
The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each o...The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.展开更多
文摘In this paper, a least-squares mixed finite element method for the solution of the primal saddle-point problem is developed. It is proved that the approximate problem is consistent ellipticity in the conforming finite element spaces with only the discrete BB-condition needed for a smaller auxiliary problem. The abstract error estimate is derived. [ABSTRACT FROM AUTHOR]
文摘The wave period probability densities in non-Gaussian mixed sea states are calculated by utilizing a transformed Gaussian process method. The transformation relating the non-Gaussian process and the original Gaussian process is obtained based on the equivalence of the level up-crossing rates of the two processes. A saddle point approximation procedure is applied for calculating the level up-crossing rates in this study. The accuracy and efficiency of the transformed Gaussian process method are validated by comparing the results predicted by using the method with those predicted by the Monte Carlo simulation method.
文摘The polynomials related with cubic Hermite-Padé approximation to the exponential function are investigated which have degrees at most n, m, s respectively. A connection is given between the coefficients of each of the polynomials and certain hypergeometric functions, which leads to a simple expression for a polynomial in a special case. Contour integral representations of the polynomials are given. By using of the saddle point method the exact asymptotics of the polynomials are derived as n, m, s tend to infinity through certain ray sequence. Some further uniform asymptotic aspects of the polynomials are also discussed.
