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.
Additional Metadata  

galerkin methods, twopoint boundary problems, lobatto points  
Partial differential equations, boundary value problems (msc 65Nxx)  
Springer  
Numerische Mathematik  
Bakker, M. (1982). A note on Co Galerkin methods for twopoint boundary problems . Numerische Mathematik, 38(3), 447â453.
