Higher-order finite element methods

By: Šolin, PavelContributor(s): Segeth, Karel | Doležel, IvoMaterial type: TextTextPublication details: Boca Raton, FL : Chapman & Hall/CRC, c2004Description: xx, 382 p. : illustrations ; 1 CD-ROM (4 3/4 in.)ISBN: 158488438X; 9781584884385Subject(s): Finite element methodDDC classification: 620.001 Online resources: Click here to access online
Contents:
1. Introduction -- 2. Hierarchic master elements of arbitrary order -- 3. Higher-order finite element discretization -- 4. Higher-order numerical quadrature -- 5. Numberical solution of finite element equations -- Mesh optimization, reference solutions and hp-adaptivity -- References -- Author index -- Subject index.
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.
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Reference Books Reference Books Main Library
Reference 		Reference 620.001 SOL (Browse shelf(Opens below)) Available 011292
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Included Index.

1. Introduction --
2. Hierarchic master elements of arbitrary order --
3. Higher-order finite element discretization --
4. Higher-order numerical quadrature --
5. Numberical solution of finite element equations --
Mesh optimization, reference solutions and hp-adaptivity --
References --
Author index --
Subject index.

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.

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