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Adams, R.A. and Fournier, J.J.F. (2003) Sobolev Spaces. 2nd Edition, Academic Press, New York.

has been cited by the following article:

• TITLE: A Numerical Approach to a Nonlinear and Degenerate Parabolic Problem by Regularization Scheme

  AUTHORS: Haitao Cao

  KEYWORDS: Nonlinear Degenerate Parabolic Equation, Finite Element Method, Regularization, Implicit Scheme

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.2 No.5, April 24, 2014

  ABSTRACT: In this work we propose a numerical scheme for a nonlinear and degenerate parabolic problem having application in petroleum reservoir and groundwater aquifer simulation. The degeneracy of the equation includes both locally fast and slow diffusion (i.e. the diffusion coefficients may explode or vanish in some point). The main difficulty is that the true solution is typically lacking in regularity. Our numerical approach includes a regularization step and a standard discretization procedure by means of C0-piecewise linear finite elements in space and backward-differences in time. Within this frame work, we analyze the accuracy of the scheme by using an integral test function and obtain several error estimates in suitable norms.