Coverart for item
The Resource Numerical methods for PDEs : state of the art techniques, Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia, editors

Numerical methods for PDEs : state of the art techniques, Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia, editors

Label
Numerical methods for PDEs : state of the art techniques
Title
Numerical methods for PDEs
Title remainder
state of the art techniques
Statement of responsibility
Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia, editors
Contributor
Editor
Subject
Language
eng
Member of
Cataloging source
N$T
Dewey number
515.353
Illustrations
illustrations
Index
no index present
LC call number
QA374
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1967-
http://library.link/vocab/relatedWorkOrContributorName
  • Di Pietro, Daniele Antonio
  • Ern, Alexandre
  • Formaggia, L.
Series statement
SEMA SIMAI Springer series,
Series volume
volume 15
http://library.link/vocab/subjectName
Differential equations, Partial
Label
Numerical methods for PDEs : state of the art techniques, Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia, editors
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Acknowledgements; Contents; About the Editors; 1 An Introduction to Recent Developments in Numerical Methods for Partial Differential Equations; References; 2 An Introduction to the Theory of M-Decompositions; 2.1 Introduction; 2.2 What Motivated the Appearance of the M-Decompositions?; 2.2.1 DG Methods; 2.2.2 HDG Methods; 2.2.3 Local Spaces or Stabilization Functions; 2.3 The M-Decompositions; 2.3.1 Definition; 2.3.2 The HDG-Projection; 2.3.3 Estimates of the Projection of the Errors; 2.3.4 Local Postprocessing; 2.3.5 Approximation Properties of the HDG-Projection
  • 2.4 A Construction of M-Decompositions2.4.1 A Characterization of M-Decompositions; 2.4.2 The General Construction; 2.5 Examples; 2.5.1 An Illustration of the Construction; 2.5.2 Triangular and Quadrilateral Elements; 2.5.3 General Polygonal Elements; 2.6 Extensions; Appendix: Proof of the Characterization of M-Decompositions; References; 3 Mimetic Spectral Element Method for Anisotropic Diffusion; 3.1 Introduction; 3.1.1 Overview of Standard Discretizations; 3.1.2 Overview of Mimetic Discretizations; 3.1.3 Outline of Chapter; 3.2 Anisotropic Diffusion/Darcy Problem; 3.2.1 Gradient Relation
  • 3.2.2 Divergence Relation3.2.3 Dual Grids; 3.3 Mimetic Spectral Element Method; 3.3.1 One Dimensional Spectral Basis Functions; 3.3.2 Two Dimensional Expansions; 3.3.2.1 Expanding p (Direct Formulation); 3.3.2.2 Expanding u and p (Mixed Formulation); 3.4 Transformation Rules; 3.5 Numerical Results; 3.5.1 Manufactured Solution; 3.5.2 The Sand-Shale System; 3.5.3 The Impermeable-Streak System; 3.6 Future Work; References; 4 An Introduction to Hybrid High-Order Methods; 4.1 Introduction; 4.2 Discrete Setting; 4.2.1 Polytopal Mesh; 4.2.2 Regular Mesh Sequences; 4.2.3 Local and Broken Spaces
  • 4.2.4 Projectors on Local Polynomial Spaces4.2.4.1 L2-Orthogonal Projector; 4.2.4.2 Elliptic Projector; 4.2.4.3 Approximation Properties; 4.3 Basic Principles of Hybrid High-Order Methods; 4.3.1 Local Construction; 4.3.1.1 Computing the Local Elliptic Projection from L2-Projections; 4.3.1.2 Local Space of Degrees of Freedom; 4.3.1.3 Potential Reconstruction Operator; 4.3.1.4 Local Contribution; 4.3.1.5 Consistency Properties of the Stabilization for Smooth Functions; 4.3.2 Discrete Problem; 4.3.2.1 Global Spaces of Degrees of Freedom; 4.3.2.2 Global Bilinear Form
  • 4.3.2.3 Discrete Problem and Well-Posedness4.3.2.4 Implementation; 4.3.2.5 Local Conservation and Flux Continuity; 4.3.3 A Priori Error Analysis; 4.3.3.1 Energy Error Estimate; 4.3.3.2 Convergence of the Jumps; 4.3.3.3 L2-Error Estimate; 4.3.4 A Posteriori Error Analysis; 4.3.4.1 Error Upper Bound; 4.3.4.2 Error Lower Bound; 4.3.5 Numerical Examples; 4.3.5.1 Two-Dimensional Test Case; 4.3.5.2 Three-Dimensional Test Case; 4.3.5.3 Three-Dimensional Case with Adaptive Mesh Refinement; 4.4 A Nonlinear Example: The p-Laplace Equation; 4.4.1 Discrete W1,p-Norms and Sobolev Embeddings
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319946757
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color)
http://library.link/vocab/ext/overdrive/overdriveId
com.springer.onix.9783319946764
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1057018522
  • (OCoLC)1057018522
Label
Numerical methods for PDEs : state of the art techniques, Daniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia, editors
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Acknowledgements; Contents; About the Editors; 1 An Introduction to Recent Developments in Numerical Methods for Partial Differential Equations; References; 2 An Introduction to the Theory of M-Decompositions; 2.1 Introduction; 2.2 What Motivated the Appearance of the M-Decompositions?; 2.2.1 DG Methods; 2.2.2 HDG Methods; 2.2.3 Local Spaces or Stabilization Functions; 2.3 The M-Decompositions; 2.3.1 Definition; 2.3.2 The HDG-Projection; 2.3.3 Estimates of the Projection of the Errors; 2.3.4 Local Postprocessing; 2.3.5 Approximation Properties of the HDG-Projection
  • 2.4 A Construction of M-Decompositions2.4.1 A Characterization of M-Decompositions; 2.4.2 The General Construction; 2.5 Examples; 2.5.1 An Illustration of the Construction; 2.5.2 Triangular and Quadrilateral Elements; 2.5.3 General Polygonal Elements; 2.6 Extensions; Appendix: Proof of the Characterization of M-Decompositions; References; 3 Mimetic Spectral Element Method for Anisotropic Diffusion; 3.1 Introduction; 3.1.1 Overview of Standard Discretizations; 3.1.2 Overview of Mimetic Discretizations; 3.1.3 Outline of Chapter; 3.2 Anisotropic Diffusion/Darcy Problem; 3.2.1 Gradient Relation
  • 3.2.2 Divergence Relation3.2.3 Dual Grids; 3.3 Mimetic Spectral Element Method; 3.3.1 One Dimensional Spectral Basis Functions; 3.3.2 Two Dimensional Expansions; 3.3.2.1 Expanding p (Direct Formulation); 3.3.2.2 Expanding u and p (Mixed Formulation); 3.4 Transformation Rules; 3.5 Numerical Results; 3.5.1 Manufactured Solution; 3.5.2 The Sand-Shale System; 3.5.3 The Impermeable-Streak System; 3.6 Future Work; References; 4 An Introduction to Hybrid High-Order Methods; 4.1 Introduction; 4.2 Discrete Setting; 4.2.1 Polytopal Mesh; 4.2.2 Regular Mesh Sequences; 4.2.3 Local and Broken Spaces
  • 4.2.4 Projectors on Local Polynomial Spaces4.2.4.1 L2-Orthogonal Projector; 4.2.4.2 Elliptic Projector; 4.2.4.3 Approximation Properties; 4.3 Basic Principles of Hybrid High-Order Methods; 4.3.1 Local Construction; 4.3.1.1 Computing the Local Elliptic Projection from L2-Projections; 4.3.1.2 Local Space of Degrees of Freedom; 4.3.1.3 Potential Reconstruction Operator; 4.3.1.4 Local Contribution; 4.3.1.5 Consistency Properties of the Stabilization for Smooth Functions; 4.3.2 Discrete Problem; 4.3.2.1 Global Spaces of Degrees of Freedom; 4.3.2.2 Global Bilinear Form
  • 4.3.2.3 Discrete Problem and Well-Posedness4.3.2.4 Implementation; 4.3.2.5 Local Conservation and Flux Continuity; 4.3.3 A Priori Error Analysis; 4.3.3.1 Energy Error Estimate; 4.3.3.2 Convergence of the Jumps; 4.3.3.3 L2-Error Estimate; 4.3.4 A Posteriori Error Analysis; 4.3.4.1 Error Upper Bound; 4.3.4.2 Error Lower Bound; 4.3.5 Numerical Examples; 4.3.5.1 Two-Dimensional Test Case; 4.3.5.2 Three-Dimensional Test Case; 4.3.5.3 Three-Dimensional Case with Adaptive Mesh Refinement; 4.4 A Nonlinear Example: The p-Laplace Equation; 4.4.1 Discrete W1,p-Norms and Sobolev Embeddings
Dimensions
unknown
Extent
1 online resource
File format
unknown
Form of item
online
Isbn
9783319946757
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations (some color)
http://library.link/vocab/ext/overdrive/overdriveId
com.springer.onix.9783319946764
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1057018522
  • (OCoLC)1057018522

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