Abstract
In this paper, we present the first reduced basis method well-suited for the
collocation framework. Two fundamentally different algorithms are presented:
the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical
Reduced Collocation Method (ERCM). This work provides a reduced basis strategy
to practitioners who {prefer} a collocation, rather than Galerkin, approach.
Furthermore, the empirical reduced collocation method eliminates a potentially
costly online procedure that is needed for non-affine problems with Galerkin
approach. Numerical results demonstrate the high efficiency and accuracy of the
reduced collocation methods, which match or exceed that of the traditional
reduced basis method in the Galerkin framework.