On the norm of the hyperinterpolation operator on the unit disk and its use for the solution of the nonlinear Poisson equation
نویسندگان
چکیده
In this article we study the properties of the hyperinterpolation operator on the unit disk D in R. We show how the hyperinterpolation can be used in connection with the Kumar-Sloan method to approximate the solution of a nonlinear Poisson equation on the unit disk (discrete Galerkin method). A bound for the norm of the hyperinterpolation operator in the space C(D) is derived. Our results prove the convergence of the discrete Galerkin method in the maximum norm if the solution of the Poisson equation is in the class C (D), > 0. Finally we present numerical examples which show that the discrete Galerkin method converges faster than O(n ), for every k 2 N, if the solution of the nonlinear Poisson equation in is C1(D). Keywords: Hyperinterpolation operator, discrete Galerkin method, projector norm, nonlinear Poisson equation AMS subject classi cation: 65R20, 65N35, 35J60, 41A55.
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On the norm of the hyperinterpolation operator on the unit disk
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