Higher-order Discrete Maximum Principle for 1d Diffusion-reaction Problems
نویسنده
چکیده
Sufficient conditions for the validity of the discrete maximum principle (DMP) for a 1D diffusion-reaction problem −u + κu = f with the homogeneous Dirichlet boundary conditions discretized by the higher-order finite element method are presented. It is proved that the DMP is satisfied if the lengths h of all elements are shorter then one-third of the length of the entire domain and if κh is small enough. The bounds for κh are precisely specified in terms of the relative length of the elements. The obtained conditions are simple and easy to verify.
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تاریخ انتشار 2007