Error Estimates for a Time Discretization Method for the Richards' Equation |
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| Authors: | Iuliu Sorin Pop |
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| Institution: | (1) Department of Mathematics and Computer Science, Technical University Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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| Abstract: | We present a numerical analysis of a time discretization method applied to Richards' equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is based on an implicit Euler time discretization scheme and includes a regularization step, combined with the Kirchhoff transform. Convergence is shown by obtaining error estimates in terms of the time step and of the regularization parameter. |
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| Keywords: | degenerate parabolic problem error estimates implicit scheme regularization Richards' equation |
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