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A monotone finite volume method for time fractional Fokker-Planck equations
Science China Mathematics, 2017We develop a monotone finite volume method for the time fractional Fokker-Planck equations and theoretically prove its unconditional stability. We show that the convergence rate of this method is of order 1 in the space and if the space grid becomes ...
Yingjun Jiang, Xuejun Xu
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2019
The one-dimensional shallow water equations (SWE), or Saint-Venant equations, are a system of nonlinear hyperbolic conservations laws (Toro, Shock-capturing methods for free surface shallow flows. Wiley, Singapore, 2001). The mathematical meaning behind these “surnames” linked to the development of Saint-Venant is clearly elucidated by the definitions (
Joel H. Ferziger +2 more
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The one-dimensional shallow water equations (SWE), or Saint-Venant equations, are a system of nonlinear hyperbolic conservations laws (Toro, Shock-capturing methods for free surface shallow flows. Wiley, Singapore, 2001). The mathematical meaning behind these “surnames” linked to the development of Saint-Venant is clearly elucidated by the definitions (
Joel H. Ferziger +2 more
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Nonconforming Finite Volume Methods
Computational Geosciences, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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2001
In Chapter 3, we saw how to derive finite-difference approximations to arbitrary derivatives. In Chapter 4, we saw that the application of a finite-difference approximation to the spatial derivatives in our model PDE’s produces a coupled set of ODE’s.
H. Lomax +2 more
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In Chapter 3, we saw how to derive finite-difference approximations to arbitrary derivatives. In Chapter 4, we saw that the application of a finite-difference approximation to the spatial derivatives in our model PDE’s produces a coupled set of ODE’s.
H. Lomax +2 more
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2021
Finite-volume methods (FVM)—sometimes also called box methods—are mainly employed for the numerical solution of problems in fluid mechanics, where they were introduced in the 1970s by McDonald, MacCormack, and Paullay. However, the application of the FVM is not limited to flow problems.
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Finite-volume methods (FVM)—sometimes also called box methods—are mainly employed for the numerical solution of problems in fluid mechanics, where they were introduced in the 1970s by McDonald, MacCormack, and Paullay. However, the application of the FVM is not limited to flow problems.
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2012
Beside the finite difference and finite element methods, a new numerical method has been recently proposed, which looks to be very promising for stable and reliable solutions of the fundamental differential equation of pollutant transport. It is the finite volume method, which is the object of advanced research, in view of the improvements that are ...
Marcello Benedini, George Tsakiris
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Beside the finite difference and finite element methods, a new numerical method has been recently proposed, which looks to be very promising for stable and reliable solutions of the fundamental differential equation of pollutant transport. It is the finite volume method, which is the object of advanced research, in view of the improvements that are ...
Marcello Benedini, George Tsakiris
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A stabilized finite volume element method for a coupled Stokes–Darcy problem
Applied Numerical Mathematics, 2017In this paper, we present a stabilized finite volume element method with the conforming finite element triples P 1 – P 0 – P 1 and P 1 – P 1 – P 1 for approximating the velocity, pressure, and hydraulic head of a coupled Stokes–Darcy problem.
Rui Li +3 more
semanticscholar +1 more source
1996
As in the previous chapter, we shall consider only the generic conservation equation for a quantity φ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point: $$\int_S \rho\phi\upsilon\,\cdot n\,{\text{d}}S = \int_S \Gamma\,{\text{grad}}
Joel H. Ferziger, Milovan Perić
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As in the previous chapter, we shall consider only the generic conservation equation for a quantity φ and assume that the velocity field and all fluid properties are known. The finite volume method uses the integral form of the conservation equation as the starting point: $$\int_S \rho\phi\upsilon\,\cdot n\,{\text{d}}S = \int_S \Gamma\,{\text{grad}}
Joel H. Ferziger, Milovan Perić
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2014
The finite volume method is a very popular method for the space discretization of partial differential problems in conservation form. For an in-depth presentation of the method, we suggest the monographs [LeV02a], [Wes01] and [Tor09].
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The finite volume method is a very popular method for the space discretization of partial differential problems in conservation form. For an in-depth presentation of the method, we suggest the monographs [LeV02a], [Wes01] and [Tor09].
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2018
One major difference between the finite difference method (FDM) and the finite volume method (FVM) is that the FVM is based on the integral form of the governing equations instead of the differential form. In the FVM, this discretization is conducted over each control volume, which endows FVM with advantages of mass conservation and unstructured meshes.
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One major difference between the finite difference method (FDM) and the finite volume method (FVM) is that the FVM is based on the integral form of the governing equations instead of the differential form. In the FVM, this discretization is conducted over each control volume, which endows FVM with advantages of mass conservation and unstructured meshes.
openaire +1 more source