03321nam a22004935i 4500 978-981-97-3434-4 DE-He213 20251030112922.0 cr nn 008mamaa 240830s2024 si | s |||| 0|eng d 9789819734344 978-981-97-3434-4 10.1007/978-981-97-3434-4 doi QA71-90 PBKS bicssc MAT041000 bisacsh PBKS thema Luo, Zhendong. author. aut http://id.loc.gov/vocabulary/relators/aut 83239 Finite Element and Reduced Dimension Methods for Partial Differential Equations [electronic resource] / by Zhendong Luo. 1st ed. 2024. Singapore : Springer Nature Singapore : Imprint: Springer, 2024. XXIII, 652 p. 108 illus., 68 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Preface -- 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. This 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. Mathematics Data processing. 65715 Differential equations. Computational Mathematics and Numerical Analysis. 66073 Differential Equations. SpringerLink (Online service) Springer Nature eBook Printed edition: 9789819734337 Printed edition: 9789819734351 Printed edition: 9789819734368 https://doi.org/10.1007/978-981-97-3434-4 ZDB-2-SMA ZDB-2-SXMS 62886 62886