Premium
An algorithm for tracing the boundary curves of mushy regions in some degenerate diffusion problems
Author(s) -
de Mottoni P.,
Santi E.,
Hadeler K.P.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080130
Subject(s) - mathematics , degenerate energy levels , boundary (topology) , diffusion , convergence (economics) , dirichlet boundary condition , zero (linguistics) , geodetic datum , mathematical analysis , tracing , boundary value problem , algorithm , physics , computer science , linguistics , philosophy , cartography , quantum mechanics , geography , economics , thermodynamics , economic growth , operating system
We present an algorithm for approximating the solution of the degenerate diffusion problem u t = (ϕ( u )) xx in (0,1) × R + (with zero Dirichlet boundary conditions, and nonnegative initial datum u 0 ), where ϕ( u ) = min { ku 1} for some ϰ > 0. The algorithm also provides an approximation for the interface curves which represent the boundary of the Mushy Region = {( x , t ): ϕ ( u ( x , t )) = 1}. The convergence of the algorithm is proved.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom