Overview PDE PDE ODE FD FD FD FV FV FV

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LogoINRIA Overview 1 PDE 1-2 PDE 2 ODE 3 FD 4 FD 5 FD 6 FV 7-8 FV 8-9 FV 10 Lectures References Roger Peyret (NICE ESSI : 89), Tim Warburton (Boston MIT : 03-05), Pierre Charrier (Bordeaux Matmeca 96-08) B. Nkonga 2009 1 / 40

  • scalar nonlinear

  • advection-diffusion equation

  • numerical methods

  • multi-dimensional extensions

  • finites volumes

  • finite difference


Publié le : mardi 19 juin 2012
Lecture(s) : 33
Source : math.unice.fr
Nombre de pages : 40
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Roger Peyret (NICE ESSI : 89), Tim Warburton (Boston MIT : 03-05), Pierre Charrier (Bordeaux Matmeca 96-08)
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Numerical Methods for PDE: Finite Differences and Finites Volumes
B. Nkonga
JAD/INRIA
2/40
2009
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4
FD for 1D scalar poisson equation (elliptic).
5
10
2
Scalar Advection-Diffusion Eqation.
3
Approximation of a Scalar 1D ODE.
Finite Difference(FD) and Finite volume(FV) : Overview
1
Modelization and Simplified models of PDE.
3/09
Scalar Nonlinear Conservation law : 1D (hyperbolic).
40
9
7
8
FV for scalar nonlinear Conservation law : 1D
FD for 1D scalar difusion equation (parabolic).
Multi-Dimensional extensions
FD for 1D scalar advection-diffusion equation.
6
1
Finite Difference(FD) and Finite volume(FV) : Overview
2
Modelization and Simplified models of PDE.
04
Plan
90/4ag02NkonB.
4
Approximation of a Scalar 1D ODE.
3
Scalar Advection-Diffusion Eqation.
6
FD for 1D scalar difusion equation (parabolic).
5
FD for 1D scalar poisson equation (elliptic).
8
Scalar Nonlinear Conservation law : 1D (hyperbolic).
7
FD for 1D scalar advection-diffusion equation.
10
Multi-Dimensional extensions
9
FV for scalar nonlinear Conservation law : 1D
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Scalar Nonlinear Conservation law : 1D (hyperbolic).
7
FD for 1D scalar advection-diffusion equation.
6
Multi-Dimensional extensions
9
FV for scalar nonlinear Conservation law : 1D
8
10
Plan
Finite Difference(FD) and Finite volume(FV) : Overview
1
Modelization and Simplified models of PDE.
/40
4
FD for 1D scalar poisson equation (elliptic).
5
FD for 1D scalar difusion equation (parabolic).
2
Scalar Advection-Diffusion Eqation.
3
Approximation of a Scalar 1D ODE.
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Finite Difference(FD) and Finite volume(FV) : Overview
/6040290noag
Scalar Nonlinear Conservation law : 1D (hyperbolic).
8
FV for scalar nonlinear Conservation law : 1D
9
FD for 1D scalar difusion equation (parabolic).
6
FD for 1D scalar advection-diffusion equation.
7
Approximation of a Scalar 1D ODE.
4
FD for 1D scalar poisson equation (elliptic).
5
Modelization and Simplified models of PDE.
2
Scalar Advection-Diffusion Eqation.
3
Multi-Dimensional extensions
10
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10
Multi-Dimensional extensions
9
FD for 1D scalar advection-diffusion equation.
6
FD for 1D scalar difusion equation (parabolic).
5
FV for scalar nonlinear Conservation law : 1D
8
Scalar Nonlinear Conservation law : 1D (hyperbolic).
7
2
Scalar Advection-Diffusion Eqation.
1
Modelization and Simplified models of PDE.
4
FD for 1D scalar poisson equation (elliptic).
3
Approximation of a Scalar 1D ODE.
/497
Plan
Finite Difference(FD) and Finite volume(FV) : Overview
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10
Multi-Dimensional extensions
9
FV for scalar nonlinear Conservation law : 1D
FD for 1D scalar difusion equation (parabolic).
6
FD for 1D scalar poisson equation (elliptic).
5
Scalar Nonlinear Conservation law : 1D (hyperbolic).
8
FD for 1D scalar advection-diffusion equation.
7
Modelization and Simplified models of PDE.
2
Finite Difference(FD) and Finite volume(FV) : Overview
1
Approximation of a Scalar 1D ODE.
4
Scalar Advection-Diffusion Eqation.
3
90/804
Plan
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9
Multi-Dimensional extensions
8
FV for scalar nonlinear Conservation law : 1D
10
5
FD for 1D scalar difusion equation (parabolic).
4
FD for 1D scalar poisson equation (elliptic).
7
Scalar Nonlinear Conservation law : 1D (hyperbolic).
6
FD for 1D scalar advection-diffusion equation.
.Nkonga2B
Finite Difference(FD) and Finite volume(FV) : Overview
Plan
Modelization and Simplified models of PDE.
1
Scalar Advection-Diffusion Eqation.
2
Approximation of a Scalar 1D ODE.
3
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-8FV8-9FV10DO3EDFF45DDFF67ViervPDw1-2E1E2PDogoLIRNIevOA200910/4B.Nkonga
Approximation of a Scalar 1D ODE.
3
FD for 1D scalar poisson equation (elliptic).
4
FD for 1D scalar difusion equation (parabolic).
5
FD for 1D scalar advection-diffusion equation.
6
0
Finite Difference(FD) and Finite volume(FV) : Overview
Plan
Modelization and Simplified models of PDE.
1
Scalar Advection-Diffusion Eqation.
2
8
FV for scalar nonlinear Conservation law : 1D
7
Scalar Nonlinear Conservation law : 1D (hyperbolic).
10
9
Multi-Dimensional extensions
10
7
Scalar Nonlinear Conservation law : 1D (hyperbolic).
6
FD for 1D scalar advection-diffusion equation.
9
Multi-Dimensional extensions
8
FV for scalar nonlinear Conservation law : 1D
3
Approximation of a Scalar 1D ODE.
2
Scalar Advection-Diffusion Eqation.
5
FD for 1D scalar difusion equation (parabolic).
4
FD for 1D scalar poisson equation (elliptic).
04/
Modelization and Simplified models of PDE.
1
Finite Difference(FD) and Finite volume(FV) : Overview
Plan
02ag1190nokN.BLoE1PDPD-2ODE2FDE3NIogOAIRvrev1wei9FV10F45DDFF67V8-VF-8
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