Error bounds for minimal energy bivariate polynomial splines

Summary. We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms.

[1]  Pia R. Pfluger,et al.  Smooth interpolation to scattered data by bivariate piecewise polynomials of odd degree , 1990, Comput. Aided Geom. Des..

[2]  R. Meyling,et al.  Approximation by cubic C 1 -splines on arbitrary triangulations , 1987 .

[3]  J. H. Bramble,et al.  Bounds for a class of linear functionals with applications to Hermite interpolation , 1971 .

[4]  Larry L. Schumaker,et al.  Macro-elements and stable local bases for splines on Clough-Tocher triangulations , 2001, Numerische Mathematik.

[5]  Thomas A. Foley,et al.  Scattered data interpolation and approximation with error bounds , 1986, Comput. Aided Geom. Des..

[6]  M. C. Lopez de Silanes,et al.  Estimations de l'erreur d'approximation sur un domaine borné deRn parDm-splines d'interpolation et d'ajustement discrètes , 1988 .

[7]  R. Franke Scattered data interpolation: tests of some methods , 1982 .

[8]  Larry L. Schumaker,et al.  On the approximation power of bivariate splines , 1998, Adv. Comput. Math..

[9]  Larry L. Schumaker,et al.  On the Approximation Power of Splines on Triangulated Quadrangulations , 1998 .

[10]  M. Lai,et al.  Scattered Data Interpolation by C 2 Quintic Splines Using Energy Minimization 1997 Scattered Data Interpolation by C 2 Quintic Splines Using Energy Minimization , 1997 .

[11]  Larry L. Schumaker,et al.  Smooth macro-elements based on Clough-Tocher triangle splits , 2002, Numerische Mathematik.

[12]  Don Hong,et al.  Stability of optimal-order approximation by bivariate splines over arbitrary triangulations , 1995 .

[13]  Larry L. Schumaker,et al.  Smooth Macro-Elements Based on Powell–Sabin Triangle Splits , 2002, Adv. Comput. Math..

[14]  Larry L. Schumaker,et al.  Minimal energy surfaces using parametric splines , 1996, Comput. Aided Geom. Des..

[15]  M. Golitschek,et al.  Norms of projectors onto spaces with Riesz bases , 2000 .

[16]  J. Douglas,et al.  The stability inLq of theL2-projection into finite element function spaces , 1974 .

[17]  Larry L. Schumaker,et al.  On Stable Local Bases for Bivariate Polynomial Spline Spaces , 2001 .

[18]  Larry L. Schumaker,et al.  Macro-elements and stable local bases for splines on Powell-Sabin triangulations , 2003, Math. Comput..