A spectral method for elliptic equations: the Dirichlet problem
نویسندگان
چکیده
Let Ω be an open, simply connected, and bounded region in R, d ≥ 2, and assume its boundary ∂Ω is smooth. Consider solving an elliptic partial differential equation Lu = f over Ω with zero Dirichlet boundary values. The problem is converted to an equivalent elliptic problem over the unit ball B, and then a spectral method is given that uses a special polynomial basis. With sufficiently smooth problem parameters, the method is shown to have very fast convergence. Numerical examples illustrate exponential convergence.
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عنوان ژورنال:
- Adv. Comput. Math.
دوره 33 شماره
صفحات -
تاریخ انتشار 2010