Reduced Basis A Posteriori Error Bounds for Symmetric Parametrized Saddle Point Problems
For researchers in reduced order modeling of saddle point problems, this provides more efficient error bounds, though it is an incremental improvement over prior work.
The paper sharpens reduced basis a posteriori error bounds for symmetric parametrized saddle point problems, achieving significantly lower effectivities and reduced computational cost compared to previous approaches.
This paper directly builds upon previous work where we introduced new reduced basis a posteriori error bounds for parametrized saddle point problems based on Brezzi's theory. We here sharpen these estimates for the special case of a symmetric problem. Numerical results provide a direct comparison with former approaches and quantify the superiority of the new developed error bounds in practice: Effectivities now decrease significantly; consequently, the proposed methods provide accurate reduced basis approximations at much less computational cost.