ORDER OF MEAN APPROXIMATION BY MIXED QUASI HERMITE-FEJER INTERPOLATION

In this paper we introduce a new kind of the mixed Hermite--Fejér interpolation with boundary condi- tions and obtain the mean approximation order.Our results include a new theorem of Varma and Prasad.Be- sides,we also get some other results about the mean approximation.

Anomalous transport driven by ion temperature gradient instability in an anisotropic deuterium-tritium plasma

In this work,the anomalous transport driven by the ion temperature gradient instability is investigated in an anisotropic deuterium-tritium(D-T)plasma.The anisotropic factorα,defined as the ratio of perpendicular temperature to parallel temperature,is introduced to describe the temperature anisotropy in the equilibrium distribution function.The linear dispersion relation in local kinetic limit is derived,and then numerically evaluated to study the dependence of mode frequency on the anisotropic factorαof D and the fraction of T particleεTby choosing three sets of typical parameters,denoted as the cyclone base case,ITER and CFETR cases.Based on the linear results,the mixing length model approximation is adopted to analyze the quasi-linear particle and energy fluxes for D and T.It is found that choosing smallαand largeεTis beneficial for the confinement of particle and energy for D and T.This work may be helpful for the estimation of turbulent transport level in the ITER and CFETR devices.

PARAMETER IDENTIFICATION BY MIXED SPECTRAL-PSEUDOSPECTRAL APPROXIMATIONS

Several mixed Legendre spectral-pseudospectral approximations and Chebyshev-Legendre ap- proximations are proposed for estimating parameters in differential equations. They are easy to be performed, and have the spectral accuracy. The numerical results coincide with those of the theoretical analysis. It is easy to generalize the proposed methods to multiple-dimensional prob- lems.

LEAST-SQUARES MIXED FINITE ELEMENT METHOD FOR SADDLE-POINT PROBLEM

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]

A MIXED VIRTUAL ELEMENT METHOD FOR THE BOUSSINESQ PROBLEM ON POLYGONAL MESHES

In this work we introduce and analyze a mixed virtual element method(mixed-VEM)for the two-dimensional stationary Boussinesq problem.The continuous formulation is based on the introduction of a pseudostress tensor depending nonlinearly on the velocity,which allows to obtain an equivalent model in which the main unknowns are given by the aforementioned pseudostress tensor,the velocity and the temperature,whereas the pressure is computed via a postprocessing formula.In addition,an augmented approach together with a fixed point strategy is used to analyze the well-posedness of the resulting continuous formulation.Regarding the discrete problem,we follow the approach employed in a previous work dealing with the Navier-Stokes equations,and couple it with a VEM for the convection-diffusion equation modelling the temperature.More precisely,we use a mixed-VEM for the scheme associated with the fluid equations in such a way that the pseudostress and the velocity are approximated on virtual element subspaces of H(div)and H^(1),respectively,whereas a VEM is proposed to approximate the temperature on a virtual element subspace of H^(1).In this way,we make use of the L^(2)-orthogonal projectors onto suitable polynomial spaces,which allows the explicit integration of the terms that appear in the bilinear and trilinear forms involved in the scheme for the fluid equations.On the other hand,in order to manipulate the bilinear form associated to the heat equations,we define a suitable projector onto a space of polynomials to deal with the fact that the diffusion tensor,which represents the thermal conductivity,is variable.Next,the corresponding solvability analysis is performed using again appropriate fixed-point arguments.Further,Strang-type estimates are applied to derive the a priori error estimates for the components of the virtual element solution as well as for the fully computable projections of them and the postprocessed pressure.The corresponding rates of convergence are also established.Finally,several numerical examples illustrating the performance of the mixed-VEM scheme and confirming these theoretical rates are presented.

MIXED FINITE ELEMENT METHODS BASED ON RIESZ-REPRESENTING OPERATORS FOR THE SHELL PROBLEM

To solve the shell problem, we propose a mixed finite element method with bubble-stabili -zation term and discrete Riesz-representation operators. It is shown that this new method is coercive, implytng the well-known X-ellipticity and the Inf-Sup condition being circumvented, and the resulting linear system is symmetrically positively definite, with a condition number being at most O(h-2). Further, an optimal error bound is attained.