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- W42645120 abstract "This chapter focuses on Dirichlet problems using subspaces with nearly zero boundary conditions. The classical Rayleigh-Ritz methods for elliptic boundary value problems with Dirichlet data assume that the approximating functions fulfill the boundary conditions exactly. In most cases, that is, when the boundary is curved, the construction of such subspaces is delicate and implies many difficulties in practice. To overcome this problem there are now known modifications of the variational principles obtained by adding appropriate boundary terms. In these cases the approximating subspaces which are used need not fulfill any boundary conditions. The chapter presents versions of the Ritz and least squares methods and shows them to be quasi-optimal. Besides the concept of nearly zero boundary values and a certain inverse assumption, a sharper condition of approximability than normally used is needed. The cubic spline functions are also discussed in the chapter." @default.
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- W42645120 date "1972-01-01" @default.
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- W42645120 title "ON DIRICHLET PROBLEMS USING SUBSPACES WITH NEARLY ZERO BOUNDARY CONDITIONS" @default.
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- W42645120 doi "https://doi.org/10.1016/b978-0-12-068650-6.50027-7" @default.
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