Finite Element Approximations of Conformal Mappings (Numerical Solution of Partial Differential Equations and Related Topics)
Takaya Tsuchiya · Kyoto University Research Information Repository (Kyoto University) · 2000
In this paper, finite element approximations of $\mathrm{c}.\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{n}\mathrm{l}\mathrm{a}^{]}\sim\mathrm{I}\mathrm{n}\mathrm{a}_{1^{)}}\mathrm{I}^{)}\mathrm{i}\mathrm{n}\mathrm{g}\mathrm{s}$ defined on the unit disk to Jordan regions are $\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{d}\rho \mathrm{r}\mathrm{e}\mathrm{d}$ .Three types of $\mathrm{t}1\mathrm{l}\mathrm{e}\mathrm{n}\mathrm{o}1' \mathrm{I}\iota 1\dot{\mathrm{c}}\mathrm{i} eg..1\mathrm{i}'/_{\lrcorner}\mathrm{a}-$ tion conditions are dealt with.In each case, convergence of the fillite $\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{I}\mathrm{n}\mathrm{e}\mathrm{n}\mathrm{t}_{\mathrm{C}\mathrm{o}\mathrm{r}}1\mathrm{f}\mathrm{o}\mathrm{J}Y\mathrm{m}\mathrm{a}^{1}1$ mappings to the exact solution is proved.