Show description

Obviously, there is much freedom in the choice of F0 and F1 , throughout this paper we employ a linear blending. Now, a Coons patch x can be defined [7] by the relation Q1 ⊕ Q2 (x) = x, where Q1 ⊕ Q2 := Q1 + Q2 − Q1 Q2 . It follows that x is of the form  T    −1 0 x(u, 0) x(u, 1) −1 x(u, v) = −  F0 (u)   x(0, v) x(0, 0) x(0, 1)   F0 (v)  . F1 (u) x(1, v) x(1, 0) x(1, 1) F1 (v) (24) (25) Partition of Unity Methods on General Domains 41 The above Coons representation can be converted into B-spline or NURBS form provided that the four boundary curves are B-spline or NURBS curves.

N. The Meshless Method (MLPG) for Domain & Bie Discretizations, Tech Science Press, 2004. 3. , Meshless methods: An overview and recent developments. Comp Meth Appl Mech Engng (1996), 139:3-47. 4. , Alonso B. Application of the GFDM to improve the approximated solution of 2nd order partial differential equations, ICCES MM 2007. 5. , Multi-level Adaptive Solutions To Boundary Value Problems, Math. , 31, 1977, pp 333 - 390. 6. , The Numerical Treatment of Differential Equations, Springer, Berlin, 1966.

F (xN )) , which is well-defined for s > d/p. The multivariate discretization measure is given as the fill distance which is the Hausdorff distance from X to Ω hX,Ω := sup min x − xj x∈Ω xj ∈X 2 (2) . , sampling inequalities involving point evaluations, for functions u ∈ Wpk (Ω) from Sobolev spaces Wpk (Ω) with 1 < p < ∞ and k > d/p, or with p = 1 and k ≥ d on domains Ω ⊂ Rd have been obtained in the last years. Narcowich, Ward and Wendland considered the case of functions with scattered zeros [12] and showed how the following results can be used in the deterministic error analysis of interpolatory numerical reconstruction processes.