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000851489 020__ $$a9783319946764$$q(electronic book)
000851489 020__ $$a3319946765$$q(electronic book)
000851489 020__ $$z9783319946757
000851489 035__ $$aSP(OCoLC)on1057018522
000851489 035__ $$aSP(OCoLC)1057018522
000851489 040__ $$aN$T$$beng$$erda$$epn$$cN$T$$dN$T$$dGW5XE$$dEBLCP$$dUKMGB$$dOCLCF
000851489 049__ $$aISEA
000851489 050_4 $$aQA374
000851489 08204 $$a515.353$$223
000851489 24500 $$aNumerical methods for PDEs :$$bstate of the art techniques /$$cDaniele Antonio Di Pietro, Alexandre Ern, Luca Formaggia, editors.
000851489 264_1 $$aCham, Switzerland :$$bSpringer,$$c2018.
000851489 300__ $$a1 online resource :$$billustrations.
000851489 336__ $$atext$$btxt$$2rdacontent
000851489 337__ $$acomputer$$bc$$2rdamedia
000851489 338__ $$aonline resource$$bcr$$2rdacarrier
000851489 4901_ $$aSEMA SIMAI Springer series,$$x2199-3041 ;$$vvolume 15
000851489 504__ $$aIncludes bibliographical references and index.
000851489 5050_ $$aIntro; Preface; Acknowledgements; Contents; About the Editors; 1 An Introduction to Recent Developments in Numerical Methods for Partial Differential Equations; References; 2 An Introduction to the Theory of M-Decompositions; 2.1 Introduction; 2.2 What Motivated the Appearance of the M-Decompositions?; 2.2.1 DG Methods; 2.2.2 HDG Methods; 2.2.3 Local Spaces or Stabilization Functions; 2.3 The M-Decompositions; 2.3.1 Definition; 2.3.2 The HDG-Projection; 2.3.3 Estimates of the Projection of the Errors; 2.3.4 Local Postprocessing; 2.3.5 Approximation Properties of the HDG-Projection
000851489 5058_ $$a2.4 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
000851489 5058_ $$a3.2.2 Divergence Relation3.2.3 Dual Grids; 3.3 Mimetic Spectral Element Method; 3.3.1 One Dimensional Spectral Basis Functions; 3.3.2 Two Dimensional Expansions; 3.3.2.1 Expanding p (Direct Formulation); 3.3.2.2 Expanding u and p (Mixed Formulation); 3.4 Transformation Rules; 3.5 Numerical Results; 3.5.1 Manufactured Solution; 3.5.2 The Sand-Shale System; 3.5.3 The Impermeable-Streak System; 3.6 Future Work; References; 4 An Introduction to Hybrid High-Order Methods; 4.1 Introduction; 4.2 Discrete Setting; 4.2.1 Polytopal Mesh; 4.2.2 Regular Mesh Sequences; 4.2.3 Local and Broken Spaces
000851489 5058_ $$a4.2.4 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
000851489 5058_ $$a4.3.2.3 Discrete Problem and Well-Posedness4.3.2.4 Implementation; 4.3.2.5 Local Conservation and Flux Continuity; 4.3.3 A Priori Error Analysis; 4.3.3.1 Energy Error Estimate; 4.3.3.2 Convergence of the Jumps; 4.3.3.3 L2-Error Estimate; 4.3.4 A Posteriori Error Analysis; 4.3.4.1 Error Upper Bound; 4.3.4.2 Error Lower Bound; 4.3.5 Numerical Examples; 4.3.5.1 Two-Dimensional Test Case; 4.3.5.2 Three-Dimensional Test Case; 4.3.5.3 Three-Dimensional Case with Adaptive Mesh Refinement; 4.4 A Nonlinear Example: The p-Laplace Equation; 4.4.1 Discrete W1,p-Norms and Sobolev Embeddings
000851489 506__ $$aAccess limited to authorized users.
000851489 588__ $$aOnline resource; title from PDF title page (viewed October 17, 2018).
000851489 650_0 $$aDifferential equations, Partial.
000851489 7001_ $$aDi Pietro, Daniele Antonio,$$eeditor.
000851489 7001_ $$aErn, Alexandre,$$d1967-$$eeditor.
000851489 7001_ $$aFormaggia, L.$$q(Luca),$$eeditor.
000851489 830_0 $$aSEMA SIMAI Springer series ;$$vv. 15.
000851489 852__ $$bebk
000851489 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-94676-4$$zOnline Access$$91397441.1
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000851489 980__ $$aBIB
000851489 982__ $$aEbook
000851489 983__ $$aOnline
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