Handbook of Computer Aided Geometric Design

Chapter 11

Finite Element Approximation with Splines

Klaus Höllig

We describe in this chapter finite element methods with uniform B-splines. These techniques do not require any grid generation and yield highly accurate approximations with relatively few parameters. They are particularly well suited in combination with spline-based geometric modeling systems.

11.1 INTRODUCTION

The finite element method has become the most widely accepted general purpose technique for a broad range of applications in continuum mechanics, fluid dynamics, field theory and other areas in engineering and mathematical physics (cf., e.g., [33,31,13]). While the label “finite element method” was first used by Clough [14], the key ideas date back much further. Ritz ...