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- W3101363733 abstract "We present and analyze a numerical framework for the approximation of nonlinear degenerate elliptic equations of the Stefan or porous medium types. This framework is based on piecewise constant approximations for the functions, which we show are essentially necessary to obtain convergence and error estimates. Convergence is established without regularity assumption on the solution. A detailed analysis is then performed to understand the design properties that enable a scheme, despite these piecewise constant approximations and the degeneracy of the model, to satisfy high-order error estimates if the solution is piecewise smooth. Numerical tests, based on continuous and discontinuous approximation methods, are provided on a variety of one- and two-dimensional problems, showing the influence on the convergence rate of the nature of the degeneracy and of the design choices." @default.
- W3101363733 created "2020-11-23" @default.
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- W3101363733 date "2020-01-01" @default.
- W3101363733 modified "2023-09-25" @default.
- W3101363733 title "High-order Mass-lumped Schemes for Nonlinear Degenerate Elliptic Equations" @default.
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- W3101363733 doi "https://doi.org/10.1137/19m1244500" @default.
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