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Finite element exterior calculus /

Arnold, Douglas N., (1954-)

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Finite element exterior calculus /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Finite element exterior calculus // Douglas N. Arnold.
Author:	Arnold, Douglas N.,
Published:	Philadelphia :Society for Industrial and Applied Mathematics, : c2018.,
Description:	xi, 120 p. :ill. ;26 cm.
Notes:	Series number from cover
[NT 15003449]:	Introduction -- Basic notions of homological algebra -- Basic notions of unbounded operators on Hilbert spaces -- Hilbert complexes -- Approximation of Hilbert complexes -- Basic notions of exterior calculus -- Finite element differential forms -- Further directions and applications
Subject:	Differential equations - Numerical solutions. -
ISBN:	9781611975536

Finite element exterior calculus /
Arnold, Douglas N.,1954-

Finite element exterior calculus /Douglas N. Arnold. - Philadelphia :Society for Industrial and Applied Mathematics,c2018. - xi, 120 p. :ill. ;26 cm. - CBMS-NSF regional conference series in applied mathematics ;93. - CBMS-NSF regional conference series in applied mathematics ;93..

Series number from cover

Includes bibliographical references (p. 113-117) and index.

Introduction -- Basic notions of homological algebra -- Basic notions of unbounded operators on Hilbert spaces -- Hilbert complexes -- Approximation of Hilbert complexes -- Basic notions of exterior calculus -- Finite element differential forms -- Further directions and applications

"Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world--wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more--are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs." --Publisher's description.

ISBN: 9781611975536US54.00

LCCN: 2018047418Subjects--Topical Terms:

533930
Differential equations
--Numerical solutions.

LC Class. No.: QA372 / .A6845 2018

Dewey Class. No.: 515/.35

Finite element exterior calculus /
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050 0 0 $a QA372 $b .A6845 2018
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100 1 $a Arnold, Douglas N., $d 1954- $3 3470107
245 1 0 $a Finite element exterior calculus / $c Douglas N. Arnold.
260 # $a Philadelphia : $b Society for Industrial and Applied Mathematics, $c c2018.
300 $a xi, 120 p. : $b ill. ; $c 26 cm.
490 1 $a CBMS-NSF regional conference series in applied mathematics ; $v 93
500 $a Series number from cover
504 $a Includes bibliographical references (p. 113-117) and index.
505 0 # $a Introduction -- Basic notions of homological algebra -- Basic notions of unbounded operators on Hilbert spaces -- Hilbert complexes -- Approximation of Hilbert complexes -- Basic notions of exterior calculus -- Finite element differential forms -- Further directions and applications
520 # $a "Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world--wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more--are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs." --Publisher's description.
650 # 0 $a Differential equations $x Numerical solutions. $3 533930
650 # 0 $a Finite element method. $3 579714
650 # 0 $a Calculus. $3 517463
650 # 0 $a Calculus of variations. $3 516604
830 0 $a CBMS-NSF regional conference series in applied mathematics ; $v 93. $3 3470108