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

作者：

Highlights：

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• Permeability identification of a nonlinear convection–diffusion equation is studied.

• The finite difference scheme for nonlinear convection–diffusion equation is given.

• A wavelet multiscale method is proposed for parameter identification.

• This method is one of multiscale inversion method.

• Numerical simulations testify the effectiveness of the wavelet multiscale method.

摘要

•Permeability identification of a nonlinear convection–diffusion equation is studied.•The finite difference scheme for nonlinear convection–diffusion equation is given.•A wavelet multiscale method is proposed for parameter identification.•This method is one of multiscale inversion method.•Numerical simulations testify the effectiveness of the wavelet multiscale method.

论文关键词：65F22,65T60,76R50,76S05,86A22,Wavelet multiscale method,Inversion,Tikhonov regularization,Nonlinear convection–diffusion equation,Porous media flow,Permeability

论文评审过程：Received 2 July 2015, Revised 17 January 2016, Accepted 23 August 2017, Available online 1 September 2017, Version of Record 14 September 2017.

论文官网地址：https://doi.org/10.1016/j.cam.2017.08.016