| Summary: | 碩士 === 國立中正大學 === 應用數學研究所 === 87 === In the thesis, first of all, we apply optimal mesh redistribution algorithm
for the Galerkin's finite element method and
the least squares finite element method
to find the asymptotic optimal mesh.
After then, we add a point to the midpoint of every subinterval,
and perform two-grid method on this new mesh.
We shall investigate some convergence properties
of two-grid method on this optimal mesh,
and compare the convergence property of two-grid method
between uniform and optimal mesh.
Our numerical results shows that the convergence rate
of two-grid method on optimal mesh is better than that on uniform mesh.
We also study the smoothing and approximation properties
via some numerical experiment.
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