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Numerical solutions of the Dirichlet problem via a density theorem
Author(s) -
Whitley Robert,
Hromadka T. V.
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100308
Subject(s) - mathematics , dirichlet distribution , subspace topology , dirichlet boundary condition , dirichlet problem , mathematical analysis , boundary value problem , norm (philosophy) , boundary (topology) , political science , law
Under mild conditions a certain subspace M , consisting of functions which are analytic in a simply connected domain Ω and continuous on the boundary Gamma;, is shown to have real parts which are dense, in the sup norm, in the set of all solutions to the Dirichlet problem for continuous boundary data. Similar results hold for L p boundary data. Numerical solutions of sample Dirichlet problems are computed. © 1994 John Wiley & Sons, Inc.