Abstract: For problems that can be described by parameterized partial differential equations, reduced basis finite element constructs basis functions on top of typical high-fidelity solutions and thus greatly reduces number of unknowns. Principles of the method is introduced and favorable features are demonstrated through heat conduction problem and neutron diffusion problem. It shows speedup of three orders of magnitude during online stage.

Key words: reduced basis, finite element method, posteriori error estimate, heat conduction, neutron diffusion