This paper is concerned with establishing a reduced-order extrapolating fi- nite volume element （FVE） format based on proper orthogonal decomposition （POD） for two-dimensional （2D） hyperbolic equations. For this...This paper is concerned with establishing a reduced-order extrapolating fi- nite volume element （FVE） format based on proper orthogonal decomposition （POD） for two-dimensional （2D） hyperbolic equations. For this purpose, a semi discrete variational format relative time and a fully discrete FVE format for the 2D hyperbolic equations are built, and a set of snapshots from the very few FVE solutions are extracted on the first very short time interval. Then, the POD basis from the snapshots is formulated, and the reduced-order POD extrapolating FVE format containing very few degrees of freedom but holding sufficiently high accuracy is built. Next, the error estimates of the reduced-order solutions and the algorithm procedure for solving the reduced-order for- mat are furnished. Finally, a numerical example is shown to confirm the correctness of theoretical conclusions. This means that the format is efficient and feasible to solve the 2D hyperbolic equations.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.11271127 and11671106)
文摘This paper is concerned with establishing a reduced-order extrapolating fi- nite volume element （FVE） format based on proper orthogonal decomposition （POD） for two-dimensional （2D） hyperbolic equations. For this purpose, a semi discrete variational format relative time and a fully discrete FVE format for the 2D hyperbolic equations are built, and a set of snapshots from the very few FVE solutions are extracted on the first very short time interval. Then, the POD basis from the snapshots is formulated, and the reduced-order POD extrapolating FVE format containing very few degrees of freedom but holding sufficiently high accuracy is built. Next, the error estimates of the reduced-order solutions and the algorithm procedure for solving the reduced-order for- mat are furnished. Finally, a numerical example is shown to confirm the correctness of theoretical conclusions. This means that the format is efficient and feasible to solve the 2D hyperbolic equations.
