非线性四阶双曲方程低阶混合元方法的超收敛分析

Abstract

Abstract:

Based on the bilinear element Q₁₁ and the Q₀₁×Q₁₀ element, a lower order conforming mixed finite element approximation scheme is proposed for nonlinear fourth-order hyperbolic equation. With the help of the known high accuracy results of the about two elements, by use of derivative delivery techniques and the post-processing technique, the superclose and superconvergence with order O(h²) for both scalar original variable u and the intermediate variable v=-Δu in H¹ norm and the flux =-▽u in (L²)² norm are derived in semi-discrete schemes through interpolation and Ritz projection approach, respectively. Meanwhile, the superclose and superconvergence with order O(h²+(Δt)²) for both u and v in HM¹ norm and ???20160405-1??? in (L²)² norm are proved in fully-discrete schemes, which cannot be deduced by the interpolation and Ritz projection alone.

Key words: Nonlinear fourth-order hyperbolic equation, Mixed finite element method, Semi-discrete and fully-discrete schemes, Superclose and superconvergence

CLC Number:

O242.21

Zhang Houchao, Shi Dongyang. Superconvergence Analysis of a Lower Order Mixed Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation[J].Acta mathematica scientia,Series A, 2016, 36(4): 656-671.

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References

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Superconvergence Analysis of a Lower Order Mixed Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation

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