Abstract
We prove that all Gradient Schemes—which include Finite Element, Mixed Finite Element, Finite Volume methods—converge uniformly in time when applied to a family of nonlinear parabolic equations which contains Richards and Stefan’s models. We also provide numerical results to confirm our theoretical analysis.
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Droniou, J., Eymard, R., Guichard, C. (2014). Uniform-in-Time Convergence of Numerical Schemes for Richards’ and Stefan’s Models. In: Fuhrmann, J., Ohlberger, M., Rohde, C. (eds) Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects. Springer Proceedings in Mathematics & Statistics, vol 77. Springer, Cham. https://doi.org/10.1007/978-3-319-05684-5_23
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DOI: https://doi.org/10.1007/978-3-319-05684-5_23
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