Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

Abstract

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.

Keywords:

• Proper orthogonal decomposition
• space–time discontinuous Galerkin method
• a priori error estimates
• unsteady diffusion convection reaction equation

AMS Subject Classifications:

• 65M15
• 65M60
• 35K20

Acknowledgements

The author thanks the referees for their helpful suggestions and comments, which lead to significant improvements in the manuscript.

Notes

No potential conflict of interest was reported by the author.