LEADER 05411nam 22006614a 450 001 9910876520603321 005 20200520144314.0 010 $a1-280-28697-0 010 $a9786610286973 010 $a0-470-35884-X 010 $a0-471-76410-8 010 $a0-471-76409-4 035 $a(CKB)1000000000355162 035 $a(EBL)242880 035 $a(SSID)ssj0000218210 035 $a(PQKBManifestationID)11186880 035 $a(PQKBTitleCode)TC0000218210 035 $a(PQKBWorkID)10212967 035 $a(PQKB)10332080 035 $a(MiAaPQ)EBC242880 035 $a(PPN)170214176 035 $a(FR-PaCSA)41001010 035 $a(OCoLC)777631785 035 $a(EXLCZ)991000000000355162 100 $a20050518d2006 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPartial differential equations and the finite element method /$fPavel Solin 210 $aHoboken, N.J. $cWiley-Interscience$dc2006 215 $a1 online resource (505 p.) 225 1 $aPure and applied mathematics 300 $aDescription based upon print version of record. 311 $a0-471-72070-4 320 $aIncludes bibliographical references (p. 461-467) and index. 327 $aPartial Differential Equations and the Finite Element Method; CONTENTS; List of Figures; LIST OF FIGURES; List of Tables; LIST OF TABLES; Preface; Acknowledgments; 1 Partial Differential Equations; 1.1 Selected general properties; 1.1.1 Classification and examples; 1.1.2 Hadamard's well-posedness; 1.1 Jacques Salomon Hadamard ( 1865-1963).; 1.2 Isolines of the solution u(x, t ) of Burger's equation.; 1.1.3 General existence and uniqueness results; 1.1.4 Exercises; 1.2 Second-order elliptic problems; 1.2.1 Weak formulation of a model problem 327 $a1.3 Johann Peter Gustav Lejeune Dirichlet (1805-1859).1.2.2 Bilinear forms, energy norm, and energetic inner product; 1.2.3 The Lax-Milgram lemma; 1.2.4 Unique solvability of the model problem; 1.2.5 Nonhomogeneous Dirichlet boundary conditions; 1.2.6 Neumann boundary conditions; 1.2.7 Newton (Robin) boundary conditions; 1.2.8 Combining essential and natural boundary conditions; 1.2.9 Energy of elliptic problems; 1.2.10 Maximum principles and well-posedness; 1.4 Maximum principle for the Poisson equation in 2D.; 1.2.11 Exercises; 1.3 Second-order parabolic problems 327 $a1.3.1 Initial and boundary conditions1.3.2 Weak formulation; 1.3.3 Existence and uniqueness of solution; 1.3.4 Exercises; 1.4 Second-order hyperbolic problems; 1.4.1 Initial and boundary conditions; 1.4.2 Weak formulation and unique solvability; 1.4.3 The wave equation; 1.4.4 Exercises; 1.5 First-order hyperbolic problems; 1.5.1 Conservation laws; 1.5.2 Characteristics; 1.5.3 Exact solution to linear first-order systems; 1.5.4 Riemann problem; 1.5 Georg Friedrich Bernhard Riemann (1826-1866).; 1.6 Propagation of discontinuity in the solution of the Riemann problem. 327 $a1.5.5 Nonlinear flux and shock formation1.5.6 Exercises; 1.7 Formation of shock in the solution u(x, t ) of Burger's equation.; 2 Continuous Elements for 1D Problems; 2.1 The general framework; 2.1.1 The Galerkin method; 2.1 Boris Grigorievich Galerkin (1871-1945).; 2.1.2 Orthogonality of error and Ce?a's lemma; 2.1.3 Convergence of the Galerkin method; 2.1.4 Ritz method for symmetric problems; 2.1.5 Exercises; 2.2 Lowest-order elements; 2.2.1 Model problem; 2.2.2 Finite-dimensional subspace Vn C V; 2.2.3 Piecewise-affine basis functions; 2.2.4 The system of linear algebraic equations 327 $a2.2 Example of a basis function vi of the space Vn2.2.5 Element-by-element assembling procedure; 2.3 Tridiagonal stiffness matrix Sn.; 2.2.6 Refinement and convergence; 2.2.7 Exercises; 2.3 Higher-order numerical quadrature; 2.3.1 Gaussian quadrature rules; 2.4 Carl Friedrich Gauss (1777-1855).; 2.3.2 Selected quadrature constants; 2.1 Gaussian quadrature on Ka, order 2k - 1 = 3.; 2.2 Gaussian quadrature on Ka, order 2k - 1 = 5.; 2.3 Gaussian quadrature on Ka, order 2k - 1 = 7.; 2.4 Gaussian quadrature on Ka, order 2k - 1 = 9.; 2.5 Gaussian quadrature on Ka, order 2k - 1 = 11. 327 $a2.3.3 Adaptive quadrature 330 $aA systematic introduction to partial differentialequations and modern finite element methods for their efficient numerical solutionPartial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral 410 0$aPure and applied mathematics (John Wiley & Sons : Unnumbered) 606 $aDifferential equations, Partial$xNumerical solutions 606 $aFinite element method 615 0$aDifferential equations, Partial$xNumerical solutions. 615 0$aFinite element method. 676 $a518/.64 700 $aSolin$b Pavel$0599763 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910876520603321 996 $aPartial differential equations and the finite element method$91021502 997 $aUNINA