語系:
繁體中文
English
說明(常見問題)
回圖書館首頁
手機版館藏查詢
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Finite elements.. II,. Galerkin appr...
~
Ern, Alexandre.
FindBook
Google Book
Amazon
博客來
Finite elements.. II,. Galerkin approximation, elliptic and mixed PDEs
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Finite elements./ by Alexandre Ern, Jean-Luc Guermond.
作者:
Ern, Alexandre.
其他作者:
Guermond, Jean-Luc.
出版者:
Cham :Springer International Publishing : : 2021.,
面頁冊數:
ix, 492 p. :ill. (some col.), digital ;24 cm.
內容註:
Part V: Weak formulations and well-posedness -- Weak formulation of model problems -- Main results on well-posedness -- Part VI: Galerkin approximation -- Basic error analysis -- Error analysis with variational crimes -- Linear algebra -- Sparse matrices -- Quadratures -- Part VII: Elliptic PDEs: conforming approximation -- Scalar second-order elliptic PDEs -- H1-conforming approximation (I) -- H1-conforming approximation (II) -- A posteriori error analysis -- The Helmholtz problem -- Part VIII: Elliptic PDEs: nonconforming approximation -- Crouzeix-Raviart approximation -- Nitsche's boundary penalty method -- Discontinuous Galerkin -- Hybrid high-order methods -- Contrasted diffusivity (I) -- Contrasted diffusivity (II) -- Part IX: Vector-valued elliptic PDEs -- Linear elasticity -- Maxwell's equations: H(curl)-approximation -- Maxwell's equations: control on the divergence -- Maxwell's equations: further topics -- Part X: Eigenvalue problems -- Symmetric elliptic eigenvalue problems -- Symmetric operators, conforming approximation -- Nonsymmetric problems -- Part XI: PDEs in mixed form -- Well-posedness for PDEs in mixed form -- Mixed finite element approximation -- Darcy's equations -- Potential and flux recovery -- Stokes equations: Basic ideas -- Stokes equations: Stable Pairs (I) -- Stokes equations: Stable pairs (II) -- Appendices -- Bijective operators in Banach spaces.
Contained By:
Springer Nature eBook
標題:
Finite element method. -
電子資源:
https://doi.org/10.1007/978-3-030-56923-5
ISBN:
9783030569235
Finite elements.. II,. Galerkin approximation, elliptic and mixed PDEs
Ern, Alexandre.
Finite elements.
II,Galerkin approximation, elliptic and mixed PDEs[electronic resource] /by Alexandre Ern, Jean-Luc Guermond. - Cham :Springer International Publishing :2021. - ix, 492 p. :ill. (some col.), digital ;24 cm. - Texts in applied mathematics,v.730939-2475 ;. - Texts in applied mathematics ;v.73..
Part V: Weak formulations and well-posedness -- Weak formulation of model problems -- Main results on well-posedness -- Part VI: Galerkin approximation -- Basic error analysis -- Error analysis with variational crimes -- Linear algebra -- Sparse matrices -- Quadratures -- Part VII: Elliptic PDEs: conforming approximation -- Scalar second-order elliptic PDEs -- H1-conforming approximation (I) -- H1-conforming approximation (II) -- A posteriori error analysis -- The Helmholtz problem -- Part VIII: Elliptic PDEs: nonconforming approximation -- Crouzeix-Raviart approximation -- Nitsche's boundary penalty method -- Discontinuous Galerkin -- Hybrid high-order methods -- Contrasted diffusivity (I) -- Contrasted diffusivity (II) -- Part IX: Vector-valued elliptic PDEs -- Linear elasticity -- Maxwell's equations: H(curl)-approximation -- Maxwell's equations: control on the divergence -- Maxwell's equations: further topics -- Part X: Eigenvalue problems -- Symmetric elliptic eigenvalue problems -- Symmetric operators, conforming approximation -- Nonsymmetric problems -- Part XI: PDEs in mixed form -- Well-posedness for PDEs in mixed form -- Mixed finite element approximation -- Darcy's equations -- Potential and flux recovery -- Stokes equations: Basic ideas -- Stokes equations: Stable Pairs (I) -- Stokes equations: Stable pairs (II) -- Appendices -- Bijective operators in Banach spaces.
This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Cea's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix-Raviart, discontinuous Galerkin, hybrid high-order methods) These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows) Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
ISBN: 9783030569235
Standard No.: 10.1007/978-3-030-56923-5doiSubjects--Topical Terms:
579714
Finite element method.
LC Class. No.: QA377 / .E763 2021
Dewey Class. No.: 518.25
Finite elements.. II,. Galerkin approximation, elliptic and mixed PDEs
LDR
:04231nmm a2200337 a 4500
001
2240086
003
DE-He213
005
20210730104338.0
006
m d
007
cr nn 008maaau
008
211111s2021 sz s 0 eng d
020
$a
9783030569235
$q
(electronic bk.)
020
$a
9783030569228
$q
(paper)
024
7
$a
10.1007/978-3-030-56923-5
$2
doi
035
$a
978-3-030-56923-5
040
$a
GP
$c
GP
041
0
$a
eng
050
4
$a
QA377
$b
.E763 2021
072
7
$a
PBK
$2
bicssc
072
7
$a
MAT034000
$2
bisacsh
072
7
$a
PBK
$2
thema
082
0 4
$a
518.25
$2
23
090
$a
QA377
$b
.E71 2021
100
1
$a
Ern, Alexandre.
$3
1566763
245
1 0
$a
Finite elements.
$n
II,
$p
Galerkin approximation, elliptic and mixed PDEs
$h
[electronic resource] /
$c
by Alexandre Ern, Jean-Luc Guermond.
260
$a
Cham :
$b
Springer International Publishing :
$b
Imprint: Springer,
$c
2021.
300
$a
ix, 492 p. :
$b
ill. (some col.), digital ;
$c
24 cm.
490
1
$a
Texts in applied mathematics,
$x
0939-2475 ;
$v
v.73
505
0
$a
Part V: Weak formulations and well-posedness -- Weak formulation of model problems -- Main results on well-posedness -- Part VI: Galerkin approximation -- Basic error analysis -- Error analysis with variational crimes -- Linear algebra -- Sparse matrices -- Quadratures -- Part VII: Elliptic PDEs: conforming approximation -- Scalar second-order elliptic PDEs -- H1-conforming approximation (I) -- H1-conforming approximation (II) -- A posteriori error analysis -- The Helmholtz problem -- Part VIII: Elliptic PDEs: nonconforming approximation -- Crouzeix-Raviart approximation -- Nitsche's boundary penalty method -- Discontinuous Galerkin -- Hybrid high-order methods -- Contrasted diffusivity (I) -- Contrasted diffusivity (II) -- Part IX: Vector-valued elliptic PDEs -- Linear elasticity -- Maxwell's equations: H(curl)-approximation -- Maxwell's equations: control on the divergence -- Maxwell's equations: further topics -- Part X: Eigenvalue problems -- Symmetric elliptic eigenvalue problems -- Symmetric operators, conforming approximation -- Nonsymmetric problems -- Part XI: PDEs in mixed form -- Well-posedness for PDEs in mixed form -- Mixed finite element approximation -- Darcy's equations -- Potential and flux recovery -- Stokes equations: Basic ideas -- Stokes equations: Stable Pairs (I) -- Stokes equations: Stable pairs (II) -- Appendices -- Bijective operators in Banach spaces.
520
$a
This book is the second volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exercises as well as solutions available from a dedicated website. The salient ideas can be addressed during lecture, with the rest of the content assigned as reading material. To engage the reader, the text combines examples, basic ideas, rigorous proofs, and pointers to the literature to enhance scientific literacy. Volume II is divided into 32 chapters plus one appendix. The first part of the volume focuses on the approximation of elliptic and mixed PDEs, beginning with fundamental results on well-posed weak formulations and their approximation by the Galerkin method. The material covered includes key results such as the BNB theorem based on inf-sup conditions, Cea's and Strang's lemmas, and the duality argument by Aubin and Nitsche. Important implementation aspects regarding quadratures, linear algebra, and assembling are also covered. The remainder of Volume II focuses on PDEs where a coercivity property is available. It investigates conforming and nonconforming approximation techniques (Galerkin, boundary penalty, Crouzeix-Raviart, discontinuous Galerkin, hybrid high-order methods) These techniques are applied to elliptic PDEs (diffusion, elasticity, the Helmholtz problem, Maxwell's equations), eigenvalue problems for elliptic PDEs, and PDEs in mixed form (Darcy and Stokes flows) Finally, the appendix addresses fundamental results on the surjectivity, bijectivity, and coercivity of linear operators in Banach spaces.
650
0
$a
Finite element method.
$3
579714
650
0
$a
Differential equations, Partial
$x
Numerical solutions.
$3
540504
650
0
$a
Functional analysis.
$3
531838
650
0
$a
Galerkin methods.
$3
704916
650
1 4
$a
Analysis.
$3
891106
650
2 4
$a
Functional Analysis.
$3
893943
700
1
$a
Guermond, Jean-Luc.
$3
3491602
710
2
$a
SpringerLink (Online service)
$3
836513
773
0
$t
Springer Nature eBook
830
0
$a
Texts in applied mathematics ;
$v
v.73.
$3
3494750
856
4 0
$u
https://doi.org/10.1007/978-3-030-56923-5
950
$a
Mathematics and Statistics (SpringerNature-11649)
筆 0 讀者評論
館藏地:
全部
電子資源
出版年:
卷號:
館藏
1 筆 • 頁數 1 •
1
條碼號
典藏地名稱
館藏流通類別
資料類型
索書號
使用類型
借閱狀態
預約狀態
備註欄
附件
W9401971
電子資源
11.線上閱覽_V
電子書
EB QA377 .E763 2021
一般使用(Normal)
在架
0
1 筆 • 頁數 1 •
1
多媒體
評論
新增評論
分享你的心得
Export
取書館
處理中
...
變更密碼
登入