The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen-...The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.展开更多
A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory(HRWENO)methods for solving conservation laws was presented by Abedian(Int.J.Numer.Meth.Fluids,94(2022),pp.583-607).To re...A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory(HRWENO)methods for solving conservation laws was presented by Abedian(Int.J.Numer.Meth.Fluids,94(2022),pp.583-607).To reconstruct the fluxes in HRWENO,the common practice of reconstructing the flux functions was employed.In this follow-up research work,an alternative formulation to reconstruct the numerical fluxes is considered.First,the solution and its derivatives are directly employed to interpolate point values at interfaces of computational cells.Afterwards,the point values at interface of cell in building block are considered to obtain numerical fluxes.In this framework,arbitrary monotone fluxes can be employed,while in HRWENO the classical practice of reconstructing flux functions can be considered only to smooth flux splitting.Also,in the process of reconstruction these type of schemes consider the effectively narrower stencil of HRWENO methods.Extensive test cases such as Euler equations of compressible gas dynamics are considered to show the good performance of the methods.展开更多
文摘The object of this paper is to establish the pointwise estimations of approximation of functions in C^1 and their derivatives by Hermite interpolation polynomials. The given orders have been proved to be exact in gen- eral.
文摘A class of finite difference Hermite radial basis functions weighted essentially non-oscillatory(HRWENO)methods for solving conservation laws was presented by Abedian(Int.J.Numer.Meth.Fluids,94(2022),pp.583-607).To reconstruct the fluxes in HRWENO,the common practice of reconstructing the flux functions was employed.In this follow-up research work,an alternative formulation to reconstruct the numerical fluxes is considered.First,the solution and its derivatives are directly employed to interpolate point values at interfaces of computational cells.Afterwards,the point values at interface of cell in building block are considered to obtain numerical fluxes.In this framework,arbitrary monotone fluxes can be employed,while in HRWENO the classical practice of reconstructing flux functions can be considered only to smooth flux splitting.Also,in the process of reconstruction these type of schemes consider the effectively narrower stencil of HRWENO methods.Extensive test cases such as Euler equations of compressible gas dynamics are considered to show the good performance of the methods.
