Summary
A framework for the numerical solution of nonlinear parabolic equations, e.g. Richard’s equation or the equation describing the movement of a viscous compressible fluid in a porous medium, are discussed. Special attention is given to problems with coefficients varying in space. The solution scheme is based on an implicit time discretization combined with Newton’s method to solve the time step problems. For the solution of the linear problems, iterative methods are used. The usage of algebraic multilevel preconditioners on structured and unstructured meshes is discussed.
This work has been supported by the SFB 359 of the Deutsche Forschungsgemeinschaft.
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© 1997 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Fuhrmann, J. (1997). On Numerical Solution Methods for Nonlinear Parabolic Problems. In: Helmig, R., Jäger, W., Kinzelbach, W., Knabner, P., Wittum, G. (eds) Modeling and Computation in Environmental Sciences. Notes on Numerical Fluid Mechanics (NNFM), vol 59. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-89565-3_15
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DOI: https://doi.org/10.1007/978-3-322-89565-3_15
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