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| موضوع: كتاب Finite Element Methods and Their Applications - Zhangxin Chen السبت 16 أغسطس 2014, 12:09 pm | |
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أخوانى فى الله أحضرت لكم كتاب Finite Element Methods and Their Applications - Zhangxin Chen
ويتناول الموضوعات الأتية :
Contents 1 Elementary Finite Elements 1 11 Introduction 2 111 A One-Dimensional Model Problem 2 112 A Two-Dimensional Model Problem 9 113 An Extension to General Boundary Conditions14 114 Programming Considerations 16 12 Sobolev Spaces 19 121 LebesgueSpaces 20 122 Weak Derivatives 21 123 Sobolev Spaces 22 124 Poincar´e’s Inequality 23 125 Duality and Negative Norms 25 13 Abstract Variational Formulation 26 131 An Abstract Formulation 26 132 The Finite Element Method28 133 Examples 30 14 Finite Element Spaces 35 141 Triangles 35 142 Rectangles 40 143 Three Dimensions 42 144 AC Element 44 15 GeneralDomains 46 16 Quadrature Rules 49 17 Finite Elements for Transient Problems 50 171 A One-Dimensional Model Problem 51 172 ASemi-Discrete Scheme in Space 52 173 Fully Discrete Schemes 55 18 Finite Elements for Nonlinear Problems58 181 Linearization Approaches 59 182 Implicit Time Approximations 60 183 Explicit Time Approximations 61 19 Approximation Theory 62 191 Interpolation Errors 62 192 Error Estimates for Elliptic Problems67 X Contents -Error Estimates 68 110 Linear SystemSolution Techniques 70 1101 Gaussian Elimination 70 1102 The Conjugate Gradient Algorithm 76 111 BibliographicalRemarks 81 112 Exercises 81 2 Nonconforming Finite Elements 87 21 Second-Order Problems 87 211 Nonconforming Finite Elements on Triangles 89 212 Nonconforming Finite Elements on Rectangles92 213 Nonconforming Finite Elements on Tetrahedra95 214 Nonconforming Finite Elements on Parallelepipeds95 215 Nonconforming Finite Elements on Prisms97 22 Fourth-Order Problems 98 221 The Morley Element 100 222 The Fraeijs de Veubeke Element 102 223 The Zienkiewicz Element 103 224 The Adini Element104 23 Nonlinear Problems 105 24 TheoreticalConsiderations 106 241 An Abstract Formulation 106 242 Applications 109 25 BibliographicalRemarks 113 26 Exercises 113 3 Mixed Finite Elements 117 31 A One-Dimensional Model Problem118 32 ATwo-DimensionalModelProblem 123 33 Extension to Boundary Conditions of Other Types 126 331 A Neumann Boundary Condition126 332 A Boundary Condition of Third Type128 34 Mixed Finite Element Spaces 128 341 Mixed Finite Element Spaces on Triangles130 342 Mixed Finite Element Spaces on Rectangles 133 343 Mixed Finite Element Spaces on Tetrahedra 136 344 Mixed Finite Element Spaces on Parallelepipeds 137 345 Mixed Finite Element Spaces on Prisms 140 35 Approximation Properties143 36 Mixed Methods for Nonlinear Problems143 37 Linear SystemSolution Techniques 145 371 Introduction 145 372 The Uzawa Algorithm 146 373 The Minimum Residual Iterative Algorithm 147 374 Alternating Direction Iterative Algorithms148 Contents XI 375 Mixed-Hybrid Algorithms 150 376 An Equivalence Relationship 152 38 TheoreticalConsiderations 154 381 An Abstract Formulation 154 382 The Mixed Finite Element Method 158 383 Examples 161 384 Construction of Projection Operators162 385 Error Estimates 164 39 BibliographicalRemarks 166 310 Exercises 167 4 Discontinuous Finite Elements173 41 Advection Problems 173 411 DGMethods 174 412 Stabilized DGMethods 178 42 Diffusion Problems 183 421 Symmetric DG Method186 422 Symmetric Interior Penalty DG Method 187 423 Non-Symmetric DG Method188 424 Non-Symmetric Interior Penalty DG Method 189 425 Remarks 192 43 Mixed Discontinuous Finite Elements 194 431 AOne-DimensionalProblem 194 432 Multi-Dimensional Problems203 433 Nonlinear Problems206 44 TheoreticalConsiderations 208 441 DGMethods 208 442 Stabilized DGMethods 210 45 BibliographicalRemarks 212 46 Exercises 212 5 Characteristic Finite Elements215 51 An Example 216 52 The Modified Method of Characteristics 218 521 A One-Dimensional Model Problem 218 522 Periodic Boundary Conditions 222 523 Extension to Multi-Dimensional Problems222 524 Discussion of a Conservation Relation224 53 The Eulerian-Lagrangian Localized Adjoint Method 226 531 A One-Dimensional Model Problem 226 532 Extension to Multi-Dimensional Problems236 54 The Characteristic MixedMethod 242 55 The Eulerian-Lagrangian Mixed Discontinuous Method 245 56 Nonlinear Problems 248 57 Remarks on Characteristic Finite Elements 250 XII Contents 58 TheoreticalConsiderations 250 59 BibliographicalRemarks 258 510 Exercises 258 6 Adaptive Finite Elements261 61 LocalGridRefinement inSpace 262 611 Regular H-Schemes 263 612 Irregular H-Schemes 265 613 Unrefinements 266 62 Data Structures 267 63 A-Posteriori Error Estimates for Stationary Problems270 631 ResidualEstimators 271 632 Local Problem-Based Estimators277 633 Averaging-Based Estimators281 634 HierarchicalBasis Estimators 283 635 Efficiency of Error Estimators 287 64 A-Posteriori Error Estimates for Transient Problems 289 65 A-Posteriori Error Estimates for Nonlinear Problems 292 66 TheoreticalConsiderations 293 661 An Abstract Theory 294 662 Applications 297 67 BibliographicalRemarks 302 68 Exercises 302 7 Solid Mechanics305 71 Introduction 305 711 Kinematics 305 712 Equilibrium 306 713 MaterialLaws 306 72 VariationalFormulations 308 721 The Displacement Form 308 722 The Mixed Form 309 73 Finite Element Methods 310 731 Finite Elements and Locking Effects 310 732 Mixed Finite Elements 311 733 Nonconforming Finite Elements 313 74 TheoreticalConsiderations 314 75 BibliographicalRemarks 319 76 Exercises 319 8 Fluid Mechanics321 81 Introduction 321 82 VariationalFormulations 323 821 The Galerkin Approach323 822 The Mixed Formulation 324 Contents XIII 83 Finite Element Methods 324 831 Galerkin Finite Elements 324 832 Mixed Finite Elements 325 833 Nonconforming Finite Elements 326 84 The Navier-Stokes Equation 329 85 TheoreticalConsiderations 330 86 BibliographicalRemarks 333 87 Exercises 333 9 Fluid Flow in Porous Media337 91 Two-Phase Immiscible Flow 338 911 The Phase Formulation 340 912 The Weighted Formulation 342 913 The GlobalFormulation 342 92 Mixed Finite Elements for Pressure 343 93 Characteristic Methods for Saturation 345 94 ANumericalExample 346 95 TheoreticalConsiderations 349 951 Analysis for the Pressure Equation 349 952 Analysis for the Saturation Equation 351 96 BibliographicalRemarks 361 97 Exercises 362 10 Semiconductor Modeling363 101 Three Semiconductor Models 364 1011 The Drift-Diffusion Model 364 1012 The Hydrodynamic Model 366 1013 The QuantumHydrodynamic Model 367 102 NumericalMethods 368 1021 The Drift-Diffusion Model 368 1022 The Hydrodynamic Model 371 1023 The QuantumHydrodynamic Model 378 103 ANumericalExample 379 104 BibliographicalRemarks 384 105 Exercises 384 A Nomenclature385 References391 Index
أتمنى أن تستفيدوا منه وأن ينال إعجابكم رابط تنزيل كتاب Finite Element Methods and Their Applications - Zhangxin Chen
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