19821001
A note on Co Galerkin methods for twopoint boundary problems
Publication
Publication
Numerische Mathematik , Volume 38  Issue 3 p. 447 453
As is known [4]. the $C^o$ Galerkin solution of a twopoint boundary problem using piecewise polynomial functions, has O($h^{2k}$ ) convergence at the knots, where $k$ is the degree of the finite element space. Also, it can be proved [5] that at specific interior points, the GaussLegendre points the gradient has O($h^{k+1}$) convergence, instead of O($h^k$). In this note, it is proved that on any segment there are $kâ1$ interior points where the Galerkin solution is of O($h^{k+2}$), one order better than the global order of convergence. These points are the Lobatto points.
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Springer  
Numerische Mathematik  
Bakker, M. (1982). A note on Co Galerkin methods for twopoint boundary problems . Numerische Mathematik, 38(3), 447â453.
