We sketch a proof that under this constraint the usual order of approximation is still possible.doi:10.1007/BFb0069132Gilbert StrangSpringer Berlin HeidelbergG. Strang, The dimension of piecewise polynomial spaces and one-sided approximation, Proc. Conf. Numerical Solution of Differential Equations (...
Piecewise Polynomial Taylor Expansions – The Generalization of Faà di Bruno's Formula We present an extension of Taylor's theorem towards nonsmooth evaluation procedures incorporating absolute value operaions. Evaluations procedures are comp... T Streubel,C Tischendorf,AOK Griewank 被引量: 0发表: ...
A.A.Pekarskii - 《Russian Academy of Sciences Sbornik Mathematics》 被引量: 1发表: 2015年 PIECEWISE-POLYNOMIAL APPROXIMATIONS OF ORLICZSOBOLEV SPACES W~mE_A We denote by π(x) the characteristi function of the interval (0, 1), πk=h-1πx/h and π(?)(x)= h-1π(x/h-j)(0≤j...
Candela, A polynomial approach to piecewise hyperbolic method, Int. J. Comput. Fluid Dyn. 17 (3) (2003) 205-217.Amat S, Busquier S, Candela V. 2003. A polynomial approach to the piecewise hyperbolic methods. Int. J. Comput. Fluid Dyn. 17: 205 - 217....
The purpose of this work is to extend earlier results concerning a discrete maximum principle for collocation methods to higher order piecewise polynomial ... EG Yanik - 《Computers & Mathematics with Applications》 被引量: 31发表: 1989年 Evaluation of boundary conditions for the gust-cascade probl...
Full-degree polynomial interpolation. 3.2 Piecewise Linear Interpolation You can create a simple picture of the data set from the last section by plotting the data twice, once with circles at the data points and once with straight lines connecting the points. The following statements produce Figure...
Orthogonal polynomials have many properties in common. The zeroes of the polynomialspn(x) are real and simple and are located within the interval [a, b]. Between any two successive zeroes ofpn(x) there lies a zero ofpn+1(x). The polynomialpn(x) is given by Rodrigues’ formula ...
The only difference (which is, indeed, fundamental) is the basis construction: The G-ROM is based on a data-driven basis, whereas the FE model is based on a universal basis (i.e., piecewise polynomial basis). The Galerkin framework used to construct G-ROMs allows us to prove fundamental...
P-Version of the Finite-Element Method (COMET X) In the p-version of the finite-element method the triangulation is fixed and the degree p of the piecewise polynomial approximation is progressively increa... I Babuska,BA Szabo,IN Katz 被引量: 424发表: 1979年 The s-version of the finite...
Moreover, in order to approximate some typical functions, we employ piecewise function approximation, where the entire domain is divided into a finite number of sub-domains and function approximation is performed for each separate sub-domain. The step by step procedure for polynomial approximation is...