000 03971nam a22005415i 4500
001 978-3-030-06173-9
003 DE-He213
005 20220801214850.0
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020 _a9783030061739
_9978-3-030-06173-9
024 7 _a10.1007/978-3-030-06173-9
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aSCI096000
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.105
_223
100 1 _aRüter, Marcus Olavi.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_940930
245 1 0 _aError Estimates for Advanced Galerkin Methods
_h[electronic resource] /
_cby Marcus Olavi Rüter.
250 _a1st ed. 2019.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2019.
300 _aXIV, 496 p. 766 illus., 179 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Applied and Computational Mechanics,
_x1860-0816 ;
_v88
505 0 _aIntroduction -- Newtonian and Eshelbian Mechanics -- Boundary Value Problems -- Galerkin Methods -- Numerical Integration -- Energy Norm A Posteriori Error Estimates -- Goal-oriented A Posteriori Error Estimates in Linearized Elasticity -- Goal-oriented A Posteriori Error Estimates in Finite Hyperelasticity -- Numerical Examples -- The Nonstandard Dyadic Product Operators -- Push-forward and Pull-back Operations -- Tensor derivatives -- A Generalized Nitsche Method -- The J-integral in Elastic FractureMechanics -- Linearizations -- Materials investigated in this monograph -- Functional Analysis—A Synopsis.
520 _aThis monograph provides a compendium of established and novel error estimation procedures applied in the field of Computational Mechanics. It also includes detailed derivations of these procedures to offer insights into the concepts used to control the errors obtained from employing Galerkin methods in finite and linearized hyperelasticity. The Galerkin methods introduced are considered advanced methods because they remedy certain shortcomings of the well-established finite element method, which is the archetypal Galerkin (mesh-based) method. In particular, this monograph focuses on the systematical derivation of the shape functions used to construct both Galerkin mesh-based and meshfree methods. The mesh-based methods considered are the (conventional) displacement-based, (dual-)mixed, smoothed, and extended finite element methods. In addition, it introduces the element-free Galerkin and reproducing kernel particle methods as representatives of a class of Galerkin meshfree methods. Including illustrative numerical examples relevant to engineering with an emphasis on elastic fracture mechanics problems, this monograph is intended for students, researchers, and practitioners aiming to increase the reliability of their numerical simulations and wanting to better grasp the concepts of Galerkin methods and associated error estimation procedures.
650 0 _aMechanics, Applied.
_93253
650 0 _aSolids.
_93750
650 0 _aMathematics—Data processing.
_931594
650 0 _aComputational intelligence.
_97716
650 1 4 _aSolid Mechanics.
_931612
650 2 4 _aComputational Science and Engineering.
_940931
650 2 4 _aComputational Intelligence.
_97716
710 2 _aSpringerLink (Online service)
_940932
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030061722
776 0 8 _iPrinted edition:
_z9783030061746
830 0 _aLecture Notes in Applied and Computational Mechanics,
_x1860-0816 ;
_v88
_940933
856 4 0 _uhttps://doi.org/10.1007/978-3-030-06173-9
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c76837
_d76837