Maximum Norm Estimate for Bivariate Spline Solutions to Second Order Elliptic Partial Differential Equations in Non-divergence Form
نویسنده
چکیده
The convergence of the bivariate spline solution to the solution of the second order elliptic PDE in non-divergence form in the maximum norm is presented in this paper. Mainly, the L∞ norm of the spline projection in the Sobolev space H 0 (Ω) ∩H 0 (Ω) is shown to be bounded, where Ω is a polygonal domain. With the boundedness of the projection, one can establish the error of the spline solution to the weak solution in the L∞ norm. The ideas of the proof can be extended to deal with other linear elliptic PDEs.
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