On optimal node and polynomial degree distribution in one-dimensional \(hp\)-FEM
We are concerned with the task of constructing an optimal higher-order finite element mesh under a constraint on the total number of degrees of freedom. The motivation for this work is to obtain a truly optimal higher-order finite element mesh that can be used to compare the quality of automatic adaptive algorithms. Minimized is the approximation error in a global norm. Optimization variables include the number of elements, positions of nodes, and polynomial degrees of elements. Optimization methods and software that we use are described, and numerical results are presented.
Keywords\(hp\)-FEM Optimal mesh Optimal polynomial degree Boundary value problem
Mathematics Subject Classification (2000)65K99 65L60 65L10 65L50
The first author is grateful to Dr. Richard (Dick) Haas for many fruitful discussions.
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