Higher-Order Finite Element Methods

Pavel Solin, Karel Segeth, Ivo Dolezel

July 28, 2003 by Chapman and Hall/CRC
Reference - 408 Pages - 202 B/W Illustrations
ISBN 9781584884385 - CAT# C438X
Series: Studies in Advanced Mathematics


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  • Offers a clear introduction and a comprehensible, detailed survey of state-of-the-art higher-order finite element methods and their practical implementation
  • Provides fast access to concrete, explicit formulae for computer implementation
  • Describes a feasible algorithmic treatment of fully automatic hp-adaptivity with examples based on original recent results
  • Includes a CD-ROM containing tables of integration points and weights for all reference domains up to order p=20
  • Summary

    The finite element method has always been a mainstay for solving engineering problems numerically. The most recent developments in the field clearly indicate that its future lies in higher-order methods, particularly in higher-order hp-adaptive schemes. These techniques respond well to the increasing complexity of engineering simulations and satisfy the overall trend of simultaneous resolution of phenomena with multiple scales.

    Higher-Order Finite Element Methods provides an thorough survey of intrinsic techniques and the practical know-how needed to implement higher-order finite element schemes. It presents the basic priniciples of higher-order finite element methods and the technology of conforming discretizations based on hierarchic elements in spaces H^1, H(curl) and H(div). The final chapter provides an example of an efficient and robust strategy for automatic goal-oriented hp-adaptivity.

    Although it will still take some time for fully automatic hp-adaptive finite element methods to become standard engineering tools, their advantages are clear. In straightforward prose that avoids mathematical jargon whenever possible, this book paves the way for fully realizing the potential of these techniques and putting them at the disposal of practicing engineers.