Galerkin approximation with proper orthogonal decomposition: new error estimates and illustrative examples (Q2842464)

The paper is concerned with the Galerkin estimates for the proper orthogonal decomposition reduction of some classical partial differential equations (PDEs). The a priori error estimates obtained by the authors are expressed in terms of projection errors. The study is carried out for the case of evolution PDEs with Lipschitz nonlinearities, or for wave-like equations. Numerical experiments presented in the second part of the paper support the theoretical findings.