Natural neighbor coordinates [20] are optimum weighted-average measures for an irregular arrangement of nodes in R. [26] used the notion of Bézier simplices in natural neighbor coordinates Φ to propose a C interpolant. The C interpolant has quadratic precision in Ω ⊂ R, and reduces to a cubic polynomial between adjacent nodes on the boundary ∂Ω. We present the C formulation and propose a comput...

This manuscript discusses the existence of nontrivial weak solution for following nonlinear eigenvalue problem driven by p(?)-biharmonic operator with Rellich-type term {?(|?u|p(x)?2?u) = ?|u|q(x)?2u/?(x)2q(x), x ? ?, u ?u 0, ??. Considering case 1 < min x?? p(x) max q(x) (N 2, Np(x) N 2p(x) ), we extend corresponding result reference [8], .p(x) 2 . The proofs main results are based on mount...

We present a new method for the solution of the Stokes equations. Our goal is to develop a robust and scalable methodology for two and three dimensional, moving-boundary, flow simulations. Our method is based on Anita Mayo’s method for the Poisson’s equation: “The Fast Solution of Poisson’s and the Biharmonic Equations on Irregular Regions”, SIAM J. Num. Anal., 21 (1984), pp. 285– 299. We embed...