example: 1d convection-diffusion equation · discretized convection-diffusion equation. ... exact...
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Shanghai Jiao Tong University
Example: 1D convection-diffusion equation
Shanghai Jiao Tong University
Discretized convection-diffusion equation
Shanghai Jiao Tong UniversityExact solution of the difference scheme
Shanghai Jiao Tong UniversityNumerical behavior of the difference scheme
Shanghai Jiao Tong UniversityEvaluation of the central difference scheme
Shanghai Jiao Tong UniversityEvaluation of the upwind difference scheme
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Finite Element Method
Shanghai Jiao Tong UniversityFinite Element Method
Shanghai Jiao Tong University
1D minimization problem
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1D minimization problem
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Du Bois Reymond lemma
Shanghai Jiao Tong University1D Poisson equation
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2D Poisson equation
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2D Poisson equation
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Rayleigh-Ritz method
Shanghai Jiao Tong University1D Poisson equation
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Poor choice of the basis functions
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Finite Element Method
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Finite Element Method
Shanghai Jiao Tong University1D Poisson equation
Shanghai Jiao Tong University1D Poisson equation
Shanghai Jiao Tong University
Existence of a minimization problem
Shanghai Jiao Tong University1D Poisson equation
Shanghai Jiao Tong UniversityLeast-squares method
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Weighted residual method
Shanghai Jiao Tong University1D Poisson equation
Shanghai Jiao Tong University2D Poisson equation
Shanghai Jiao Tong University2D Poisson equation
Shanghai Jiao Tong UniversityConstruction of 1D finite elements
Shanghai Jiao Tong UniversityConstruction of 1D finite elements
Shanghai Jiao Tong UniversityConstruction of 1D finite elements
Shanghai Jiao Tong UniversityConstruction of triangular finite elements
Shanghai Jiao Tong UniversityConstruction of triangular finite elements
Shanghai Jiao Tong UniversityConstruction of triangular finite elements
Shanghai Jiao Tong UniversityConstruction of tetrahedral finite elements
Shanghai Jiao Tong UniversityCoordinate and element transformations
Shanghai Jiao Tong UniversityCoordinate and element transformations
Shanghai Jiao Tong UniversityCoordinate and element transformations
Shanghai Jiao Tong UniversityCoordinate and element transformations
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Construction of qudarilateral finite elements
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Construction of qudarilateral finite elements
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Construction of hexahedral finite elements
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Finite elements matrix assembly
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1D Poisson equation/linear element
Shanghai Jiao Tong University
1D Poisson equation/linear element
Shanghai Jiao Tong University
1D Poisson equation/linear element
Shanghai Jiao Tong University1D Poisson equation/quadratic element
Shanghai Jiao Tong UniversityNumerical integration for finite element
Shanghai Jiao Tong UniversityStorage of space matrices
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Discretization in Time
Shanghai Jiao Tong UniversityIBV problems
Shanghai Jiao Tong UniversitySpace-time discretization
Shanghai Jiao Tong UniversityStandard time-stepping schemes
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Properties of time-stepping schemes
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Explicit vs. implicit time discretization
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1D convection-diffusion equation
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1D convection-diffusion equation
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1D convection-diffusion equation
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Fractional-step ɵ-scheme
Shanghai Jiao Tong UniversityPredictor-corrector and multipoint methods
Shanghai Jiao Tong UniversityAdams methods
Shanghai Jiao Tong UniversityAdams methods
Shanghai Jiao Tong UniversityRunge-Kutta methods
Shanghai Jiao Tong UniversityRunge-Kutta methods
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Automatic time step control
Shanghai Jiao Tong UniversityAutomatic time step control
Shanghai Jiao Tong UniversityPractical implementation
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Evolutionary PID controller
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Pseudo time-stepping
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Properties of numerical methods
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Properties of numerical methods
Shanghai Jiao Tong UniversityConsistency
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Stability
Shanghai Jiao Tong UniversityMatrix method for stability analysis
Shanghai Jiao Tong UniversityMatrix method for stability analysis
Shanghai Jiao Tong UniversityVon Neumann’s stability anaylsis
Shanghai Jiao Tong UniversityVon Neumann’s stability anaylsis
Shanghai Jiao Tong University1D pure convection equation
Shanghai Jiao Tong University1D pure convection equation
Shanghai Jiao Tong University1D pure convection equation
Shanghai Jiao Tong UniversitySpectral analysis of numerical errors
Shanghai Jiao Tong UniversityConvergency
Shanghai Jiao Tong UniversityConservation
Shanghai Jiao Tong UniversityDiscrete conservation
Shanghai Jiao Tong UniversityBoundedness