Computing with Hp-Adaptive Finite Elements: Volume 1 One and Two Dimensional Elliptic and Maxwell Problems [With CD-ROM] (Hardcover)

1D PROBLEMS1D Model Elliptic Problem A Two-Point Boundary Value ProblemAlgebraic Structure of the Variational FormulationEquivalence with a Minimization ProblemSobolev Space H1(0, l)Well Posedness of the Variational BVPExamples from Mechanics and PhysicsThe Case with "Pure Neumann" BCsExercisesGalerkin MethodFinite Dimensional Approximation of the VBVPElementary Convergence AnalysisCommentsExercises1D hp Finite Element Method1D hp DiscretizationAssembling Element Matrices into Global Matrices Computing the Element MatricesAccounting for the Dirichlet BC SummaryAssignment 1: A Dry RunExercises1D hp CodeSetting up the 1D hp CodeFundamentals GraphicsElement Routine Assignment 2: Writing Your Own ProcessorExercisesMesh Refinements in 1D The h-Extension Operator. Constrained Approximation CoefficientsProjection-Based Interpolation in 1DSupporting Mesh RefinementsData-Structure-Supporting RoutinesProgramming Bells and Whistles Interpolation Error Estimates ConvergenceAssignment 3: Studying ConvergenceDefinition of a Finite ElementExercisesAutomatic hp Adaptivity in 1DThe hp AlgorithmSupporting the Optimal Mesh Selection Exponential Convergence. Comparing with h AdaptivityDiscussion of the hp AlgorithmAlgebraic Complexity and Reliability of the AlgorithmExercisesWave Propagation ProblemsConvergence Analysis for Noncoercive ProblemsWave Propagation Problems Asymptotic Optimality of the Galerkin MethodDispersion Error AnalysisExercises2D ELLIPTIC PROBLEMS 2D Elliptic Boundary-Value ProblemClassical FormulationVariational (Weak) FormulationAlgebraic Structure of the Variational FormulationEquivalence with a Minimization Problem Examples from Mechanics and PhysicsExercisesSobolev SpacesSobolev Space H1(O)Sobolev Spaces of an Arbitrary OrderDensity and Embedding TheoremsTrace TheoremWell Posedness of the Variational BVPExercises2D hp Finite Element Method on Regular Meshes Quadrilateral Master Element Triangular Master ElementParametric ElementFinite Element Space. Construction of Basis FunctionsCalculation of Element Matrices Modified Element. Imposing Dirichlet Boundary ConditionsPostprocessing- Local Access to Element d.o.fProjection-Based InterpolationExercises2D hp Code Getting Started Data Structure in FORTRAN 90FundamentalsThe Element RoutineModified Element. Imposing Dirichlet Boundary ConditionsAssignment 4: Assembly of Global MatricesThe Case with "Pure Neumann" Boundary ConditionsGeometric Modeling and Mesh GenerationManifold Representation Construction of Compatible ParametrizationsImplicit Parametrization of a Rectangle Input File Preparation Initial Mesh GenerationThe hp Finite Element Method on h-Refined MeshesIntroduction. The h Refinements 1-Irregular Mesh Refinement Algorithm Data Structure in Fortran 90 (Continued)Constrained Approximation for C0 DiscretizationsReconstructing Element Nodal ConnectivitiesDetermining Neighbors for Midedge Nodes Additional CommentsAutomatic hp Adaptivity in 2DThe Main IdeaThe 2D hp AlgorithmExample: L-Shape Domain ProblemExample: 2D "Shock" ProblemAdditional RemarksExamples of ApplicationsA "Battery Problem" Linear ElasticityAn Axisymmetric Maxwell ProblemExercisesExterior Boundary-Value Problems Variational Formulation. Infinite Element DiscretizationSelection of IE Radial Shape FunctionsImplementationCalculation of Echo AreaNumerical ExperimentsCommentsExercises2D MAXWELL PROBLEMS2D Maxwell EquationsIntroduction to Maxwell's EquationVariational Formulation ExercisesEdge Elements and the de Rham Diagram Exact SequencesProjection-Based InterpolationDe Rham Diagram Shape FunctionsExercises2D Maxwell CodeDirectories. Data StructureThe Element RoutineConstrained Approximation. Modified ElementSetting up a Maxwell Problem Exerciseshp Adaptivity for Maxwell Equations Projection-Based Interpolation RevisitedThe hp Mesh Optimization Algorithm Example: The Screen ProblemExterior Maxwell Boundary-Value Problems Variational FormulationInfinite Element Discretization in 3DInfinite Element Discretization in 2DStabilityImplementationNumerical ExperimentsExercisesA Quick Summary and OutlookAppendixBibliographyIndex