|
" Finite element exterior calculus / "
Douglas N. Arnold, University of Minnesota, Minneapolis, Minnesota.
| Document Type
|
:
|
BL
|
| Record Number
|
:
|
854440
|
| Main Entry
|
:
|
Arnold, Douglas N.,1954-
|
| Title & Author
|
:
|
Finite element exterior calculus /\ Douglas N. Arnold, University of Minnesota, Minneapolis, Minnesota.
|
| Publication Statement
|
:
|
Philadelphia :: Society for Industrial and Applied Mathematics,, [2018]
|
|
|
:
|
, ©2018
|
| Series Statement
|
:
|
CBMS-NSF regional conference series in applied mathematics ;; 93
|
| Page. NO
|
:
|
xi, 120 pages :: illustrations ;; 26 cm.
|
| ISBN
|
:
|
1611975530
|
|
|
:
|
: 9781611975536
|
|
|
:
|
9781611975543
|
| Notes
|
:
|
Series number from cover.
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references (pages 113-117) and index.
|
| Contents
|
:
|
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.
|
| Abstract
|
:
|
"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.
|
| Subject
|
:
|
Calculus of variations.
|
| Subject
|
:
|
Calculus.
|
| Subject
|
:
|
Differential equations-- Numerical solutions.
|
| Subject
|
:
|
Finite element method.
|
| Subject
|
:
|
Calculus of variations.
|
| Subject
|
:
|
Calculus.
|
| Subject
|
:
|
Differential equations-- Numerical solutions.
|
| Subject
|
:
|
Finite element method.
|
| Dewey Classification
|
:
|
515/.35
|
| LC Classification
|
:
|
QA372.A6845 2018
|
| |