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The posteriori error estimate of finite element method based on reduced-basis method for convection-diffusion equation. (Chinese. English summary) Zbl 1349.65590

Summary: We combine the reduced-basis method and finite element method to solve partial differential equations. This method not only can reduce the dimensions of the finite element discrete scheme greatly, but also keep the high order accuracy. The memory and computing time are saved in finite element scheme based on reduced-basis method. In this paper, the Crank-Nicolson finite element approximation based on reduced-basis method for convection-diffusion equation is established, the posterior error estimate is given.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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