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020 _a9789819734344
_9978-981-97-3434-4
024 7 _a10.1007/978-981-97-3434-4
_2doi
050 4 _aQA71-90
072 7 _aPBKS
_2bicssc
072 7 _aMAT041000
_2bisacsh
072 7 _aPBKS
_2thema
100 1 _aLuo, Zhendong.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_983239
245 1 0 _aFinite Element and Reduced Dimension Methods for Partial Differential Equations
_h[electronic resource] /
_cby Zhendong Luo.
250 _a1st ed. 2024.
264 1 _aSingapore :
_bSpringer Nature Singapore :
_bImprint: Springer,
_c2024.
300 _aXXIII, 652 p. 108 illus., 68 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Basic Theory of Standard Finite Element Method -- Basic Theory of Mixed Finite Element Method -- Mixed Finite Element Methods for the Unsteady Partial Differential Equations -- The Reduced Dimension Methods of Finite Element Subspaces for Unsteady Partial Differential Equations -- The Reduced Dimension of Finite Element Solution Coefficient Vectors for Unsteady Partial Differential Equations -- Bibliography -- Index.
520 _aThis book aims to provide with some approaches for lessening the unknowns of the FE methods of unsteady PDEs. It provides a very detailed theoretical foundation of finite element (FE) and mixed finite element (MFE) methods in the first 2 chapters, and then Chapter 3 provides the FE and MFE methods to solve unsteady partial differential equations (PDEs). In the following 2 chapters, the principle and application of two proper orthogonal decomposition (POD) methods are introduced in detail. This book can be used as both the introduction of FE method and the gateway to the FE frontier. For readers who want to learn the FE and MFE methods for solving various steady and unsteady PDEs, they will find the first 3 chapters very helpful. While those who care about engineering applications may jump to the last 2 chapters that introduce the construction of dimension reduction models and their applications to practical process calculations. This part could help them to improve the calculation efficiency and save CPU runtime so as to do wonders for their engineering calculations.
650 0 _aMathematics
_xData processing.
_965715
650 0 _aDifferential equations.
650 1 4 _aComputational Mathematics and Numerical Analysis.
_966073
650 2 4 _aDifferential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9789819734337
776 0 8 _iPrinted edition:
_z9789819734351
776 0 8 _iPrinted edition:
_z9789819734368
856 4 0 _uhttps://doi.org/10.1007/978-981-97-3434-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c62886
_d62886