Boundary element collocation methods using splines with multiple knots
- McLean, William
- Prößdorf, Siegfried
2010 Mathematics Subject Classification
- 65N38 41A15 65N12 35S99 42A16
- splines with multiple knots, Symm´s equation, stability, error analysis, collocation methods, boundary integral equations, convergence, superconvergence, numerical experiments
We extend the theory of boundary element collocation methods by allowing reduced inter-element smoothness (or in other words, by allowing trial functions that are splines with multiple knots). Our convergence analysis is based on a recurrence relation for the Fourier coefficients of the numerical solution, and so is restricted to uniform grids on smooth, closed curves. Superconvergence is possible with special choices of the collocation points. Numerical experiments with a model problem confirm the convergence rates predicted by our theory.
- Numer. Math., 74 (1996), pp. 419--451