Preprint

Local Multilevel Methods on Graded Bisection Grids

Long Chen, R.H. Nochetto, and Jinchao Xu

To be submitted

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ABSTRACT:

We design and analyze optimal additive and multiplicative multilevel
methods for solving H1 problem on adaptive grids obtained by
bisection. We present a novel decomposition of spaces based on the
geometric structure of bisection grids in any dimension and use it to
bridge the gap between graded and quasi-uniform grids, for which the
multilevel theory is well-established. We show that local smoothing
for a new added node needs to be performed only for three vertices
-the new vertex and its two parents vertices- thereby leading to
optimal complexity for any dimensions and polynomial degree.