A Bernstein-Bezier Sufficient Condition for Invertibility of Polynomial Mapping Functions

We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient @� =

[1]  Claes Johnson.  Numerical solution of partial differential equations by the finite element method , 1988 .

[2]  N. Megiddo.  Linear-time algorithms for linear programming in R3 and related problems , 1982, FOCS 1982.

[3]  Nimrod Megiddo,et al.  Linear-Time Algorithms for Linear Programming in R^3 and Related Problems , 1982, FOCS.

[4]  A. Z. Salem,et al.  Mid-node admissible spaces for quadratic triangular 2D finite elements with one edge curved , 2001 .

[5]  M. Lenoir.  Optimal isoparametric finite elements and error estimates for domains involving curved boundaries , 1986 .

[6]  Herbert Edelsbrunner,et al.  Algorithms in Combinatorial Geometry , 1987, EATCS Monographs in Theoretical Computer Science.

[7]  Sunil Saigal,et al.  Mid-Node Admissible Space for 3D Quadratic Tetrahedral Finite Elements , 2001, Engineering with Computers.

[8]  Nimrod Megiddo,et al.  Linear-time algorithms for linear programming in R3 and related problems , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[9]  P. G. Ciarlet,et al.  Interpolation theory over curved elements, with applications to finite element methods , 1972 .

[10]  Fujio Yamaguchi,et al.  Curves and Surfaces in Computer Aided Geometric Design , 1988, Springer Berlin Heidelberg.

[11]  M. Shephard,et al.  Automatic Meshing of Curved Three—Dimensional Domains: Curving Finite Elements and Curvature-Based Mesh Control , 1995 .

[12]  G. Ziegler.  Lectures on Polytopes , 1994 .

[13]  A. Z. Salem,et al.  Mid-node admissible spaces for quadratic triangular arbitrarily curved 2D finite elements , 2001 .