LEADER 04157nam 2200541 450 001 996418197603316 005 20230124200757.0 010 $a3-030-55069-9 024 7 $a10.1007/978-3-030-55069-1 035 $a(CKB)4100000011528313 035 $a(MiAaPQ)EBC6382109 035 $a(DE-He213)978-3-030-55069-1 035 $a(MiAaPQ)EBC6647491 035 $a(Au-PeEL)EBL6382109 035 $a(OCoLC)1202744899 035 $a(Au-PeEL)EBL6647491 035 $a(PPN)26914644X 035 $a(EXLCZ)994100000011528313 100 $a20220318d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 13$aAn introduction to element-based Galerkin methods on tensor-product bases $eanalysis, algorithms, and applications /$fFrancis X. Giraldo 205 $a1st ed. 2020. 210 1$aCham, Switzerland :$cSpringer,$d[2020] 210 4$dİ2020 215 $a1 online resource (XXVI, 559 p. 171 illus., 168 illus. in color.) 225 1 $aTexts in Computational Science and Engineering,$x1611-0994 ;$v24 300 $aIncludes index. 311 $a3-030-55068-0 327 $aIntroduction -- Motivation and Background -- Overview of Existing Methods -- One-Dimensional Problems -- Interpolation in One Dimension -- Numerical Integration in One Dimension -- 1D Continuous Galerkin Method for Hyperbolic Equations -- 1D Discontinuous Galerkin Methods for Hyperbolic Equations -- 1D Unified Continuous and Discontinuous Galerkin Methods for Systems of Hyperbolic Equations -- 1D Continuous Galerkin Methods for Elliptic Equations -- 1D Discontinuous Galerkin Methods for Elliptic Equations -- Two-Dimensional Problems -- Interpolation in Multiple Dimensions -- Numerical Integration in Multiple Dimensions -- 2D Continuous Galerkin Methods for Elliptic Equations -- 2D Discontinuous Galerkin Methods for Elliptic Equations -- 2D Unified Continuous and Discontinuous Galerkin Methods for Elliptic Equations -- 2D Continuous Galerkin Methods for Hyperbolic Equations -- 2D Discontinuous Galerkin Methods for Hyperbolic Equations -- 2D Continuous/Discontinuous Galerkin Methods for Hyperbolic Equations -- Advanced Topics -- Stabilization of High-Order Methods -- Adaptive Mesh Refinement -- Time Integration -- 1D Hybridizable Discontinuous Galerkin Method -- Classification of Partial Differential Equations and Vector Notation -- Jacobi Polynomials -- Data Structures. 330 $aThis book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function spaces), the book?s main focus is on how to build the method, what the resulting matrices look like, and how to write algorithms for coding Galerkin methods. In addition, the spotlight is on tensor-product bases, which means that only line elements (in one dimension), quadrilateral elements (in two dimensions), and cubes (in three dimensions) are considered. The types of Galerkin methods covered are: continuous Galerkin methods (i.e., finite/spectral elements), discontinuous Galerkin methods, and hybridized discontinuous Galerkin methods using both nodal and modal basis functions. In addition, examples are included (which can also serve as student projects) for solving hyperbolic and elliptic partial differential equations, including both scalar PDEs and systems of equations. 410 0$aTexts in Computational Science and Engineering,$x1611-0994 ;$v24 606 $aDifferential equations, Partial$xNumerical solutions 606 $aComputer science$xMathematics 615 0$aDifferential equations, Partial$xNumerical solutions. 615 0$aComputer science$xMathematics. 676 $a515.353 700 $aGiraldo$b Francis X.$0845465 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418197603316 996 $aAn Introduction to Element-Based Galerkin Methods on Tensor-Product Bases$91887118 997 $aUNISA