02986nam a22004095i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001700165072002300182072001600205100007600221245012700297250001800424264007200442300006800514336002600582337002600608338003600634347002400670505043600694520108801130650003402218650002802252650005402280650002802334710003402362773002602396776003602422776003602458776003602494856004602530978-981-97-3434-4DE-He21320251030112922.0cr nn 008mamaa240830s2024    si |    s    |||| 0|eng d  a97898197343447 a10.1007/978-981-97-3434-42doi 4aQA71-90 7aPBKS2bicssc 7aMAT0410002bisacsh 7aPBKS2thema1 aLuo, Zhendong.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aFinite Element and Reduced Dimension Methods for Partial Differential Equationsh[electronic resource] /cby Zhendong Luo.  a1st ed. 2024. 1aSingapore :bSpringer Nature Singapore :bImprint: Springer,c2024.  aXXIII, 652 p. 108 illus., 68 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 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.  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. 0aMathematicsxData processing. 0aDifferential equations.14aComputational Mathematics and Numerical Analysis.24aDifferential Equations.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978981973433708iPrinted edition:z978981973435108iPrinted edition:z978981973436840uhttps://doi.org/10.1007/978-981-97-3434-4