SUPG reduced order models for convection-dominated convection-diffusion-reaction equations. (English) Zbl 1425.65111
Summary: This paper presents a Streamline-Upwind Petrov-Galerkin (SUPG) reduced order model (ROM) based on proper orthogonal decomposition (POD). This ROM is investigated theoretically and numerically for convection-dominated convection-diffusion-reaction problems. The SUPG finite element method was used on realistic meshes for computing the snapshots, leading to some noise in the POD data. Numerical analysis is used to propose the scaling of the stabilization parameter for the SUPG-ROM. Two approaches are used: One based on the underlying finite element discretization and the other one based on the POD truncation. The resulting SUPG-ROMs and the standard Galerkin ROM (G-ROM) are studied numerically. For many settings, the results obtained with the SUPG-ROMs are more accurate. Finally, one of the choices for the stabilization parameter is recommended.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
| 35K57 | Reaction-diffusion equations |
Keywords:
reduced order models (ROMs); convection-dominated equations; streamline-upwind Petrov-Galerkin (SUPG) method; proper orthogonal decomposition (POD); stabilization parameterSoftware:
MooNMDReferences:
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