Abstract
Based on Chebyshev–Gauss–Lobatto points, the piecewise linear finite element preconditioner is analyzed in terms of condition numbers for the high-order element discretizations applied to a model elliptic operator. The optimality of such a preconditioner is proved for one-dimensional case and the scalability is shown for two-dimensional case. Further, we provide O ( N 1 / 3 ) growth of piecewise linear finite element preconditioner numerically.
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