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Numerical methods with interface estimates for the porous medium equation. (English) Zbl 0633.76095
The numerical approximation of the porous-medium equation is studied. An \(L^{\infty}\) error bound is obtained, in terms of the Hölder exponent of the solution, and of the weak truncation error (defined in Introduction). The estimation of the difference between the numerical boundary and the true interface of the support of the solution, is obtained, using a natural numerical boundary. The results are used for the simplest finite-difference scheme based directly on the equation.
Reviewer: G.Pasa
MSC:
76S05 Flows in porous media; filtration; seepage
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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