A reduced-order extrapolation algorithm based on CNLSMFE formulation and POD technique for two-dimensional Sobolev equations

摘要

A reduced-order extrapolation algorithm based on Crank-Nicolson least-squares mixed finite element(CNLSMFE) formulation and proper orthogonal decomposition(POD)technique for two-dimensional(2D) Sobolev equations is establishedThe error estimates of the reduced-order CNLSMFE solutions and the implementation for the reduced-order extrapolation algorithm are providedA numerical example is used to show that the results of numerical computations are consistent with theoretical conclusionsMoreover, it is shown that the reduced-order extrapolation algorithm is feasible and efficient for seeking numerical solutions to2D Sobolev equations.