A wavelet multiscale method for the inverse problem of a nonlinear convection–diffusion equation

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

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Two-grid variational multiscale method with bubble stabilization for convection diffusion equation

Applied Mathematical Modelling ◽

10.1016/j.apm.2015.06.023 ◽

2016 ◽

Vol 40 (2) ◽

pp. 1097-1109 ◽

Cited By ~ 2

Author(s):

Zhifeng Weng ◽

Jerry Zhijian Yang ◽

Xiliang Lu

Keyword(s):

Diffusion Equation ◽

Multiscale Method ◽

Variational Multiscale Method ◽

Convection Diffusion ◽

Variational Multiscale ◽

Convection Diffusion Equation

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Finite point method of nonlinear convection diffusion equation

Filomat ◽

10.2298/fil2005517q ◽

2020 ◽

Vol 34 (5) ◽

pp. 1517-1533

Author(s):

Xinqiang Qin ◽

Gang Hu ◽

Gaosheng Peng

Keyword(s):

Diffusion Equation ◽

Domain Size ◽

Nonlinear Flow ◽

Step Size ◽

Finite Point ◽

Nonlinear Convection ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

Numerical Oscillations ◽

The One

Aiming at the nonlinear convection diffusion equation with the numerical oscillations, a numerical stability algorithm is constructed. The basic principle of the finite point algorithm is given and the computational scheme of the nonlinear convection diffusion equation is deduced. Then, the numerical simulation of the one-dimensional and two-dimensional nonlinear convection-dominated diffusion equation is carried out. The relationship between the calculation result and the support domain size, step size and time is discussed. The results show that the algorithm has the characteristics of simplicity, stability and efficiency. Compared with the traditional finite element method and finite difference method, the new algorithm can attain a higher calculation accuracy. Simultaneously, it proves that the method given in this paper is effective to solve the nonlinear flow diffusion equation and can eliminate the numerical oscillations.

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Stability estimate for an inverse problem of the convection-diffusion equation

Journal of Inverse and Ill-Posed Problems ◽

10.1515/jiip-2018-0072 ◽

2020 ◽

Vol 28 (1) ◽

pp. 71-92

Author(s):

Mourad Bellassoued ◽

Imen Rassas

Keyword(s):

Inverse Problem ◽

Diffusion Equation ◽

Scalar Potential ◽

Stability Estimate ◽

Inverse Boundary ◽

Convection Diffusion ◽

Convection Diffusion Equation ◽

First Order ◽

Order Coefficient ◽

Dirichlet To Neumann Map

AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

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