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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
Shanghai Jiao Tong University
Finite Element Method
Shanghai Jiao Tong UniversityFinite Element Method
Shanghai Jiao Tong University
1D minimization problem
Shanghai Jiao Tong University
1D minimization problem
Shanghai Jiao Tong University
Du Bois Reymond lemma
Shanghai Jiao Tong University1D Poisson equation
Shanghai Jiao Tong University
2D Poisson equation
Shanghai Jiao Tong University
2D Poisson equation
Shanghai Jiao Tong University
Rayleigh-Ritz method
Shanghai Jiao Tong University1D Poisson equation
Shanghai Jiao Tong University
Poor choice of the basis functions
Shanghai Jiao Tong University
Finite Element Method
Shanghai Jiao Tong University
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
Shanghai Jiao Tong University
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
Shanghai Jiao Tong University
Construction of qudarilateral finite elements
Shanghai Jiao Tong University
Construction of qudarilateral finite elements
Shanghai Jiao Tong University
Construction of hexahedral finite elements
Shanghai Jiao Tong University
Finite elements matrix assembly
Shanghai Jiao Tong University
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
Shanghai Jiao Tong University
Discretization in Time
Shanghai Jiao Tong UniversityIBV problems
Shanghai Jiao Tong UniversitySpace-time discretization
Shanghai Jiao Tong UniversityStandard time-stepping schemes
Shanghai Jiao Tong University
Properties of time-stepping schemes
Shanghai Jiao Tong University
Explicit vs. implicit time discretization
Shanghai Jiao Tong University
1D convection-diffusion equation
Shanghai Jiao Tong University
1D convection-diffusion equation
Shanghai Jiao Tong University
1D convection-diffusion equation
Shanghai Jiao Tong University
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
Shanghai Jiao Tong University
Automatic time step control
Shanghai Jiao Tong UniversityAutomatic time step control
Shanghai Jiao Tong UniversityPractical implementation
Shanghai Jiao Tong University
Evolutionary PID controller
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Pseudo time-stepping
Shanghai Jiao Tong University
Properties of numerical methods
Shanghai Jiao Tong University
Properties of numerical methods
Shanghai Jiao Tong UniversityConsistency
Shanghai Jiao Tong University
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
