Discrete maximum principle for higher-order finite elements in 1D
نویسندگان
چکیده
منابع مشابه
Discrete maximum principle for higher-order finite elements in 1D
We formulate a sufficient condition on the mesh under which we prove the discrete maximum principle (DMP) for the one-dimensional Poisson equation with Dirichlet boundary conditions discretized by the hp-FEM. The DMP holds if a relative length of every element K in the mesh is bounded by a value H∗ rel(p) ∈ [0.9, 1], where p ≥ 1 is the polynomial degree of the element K. The values H∗ rel(p) ar...
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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 sma...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2007
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-07-02022-4