一类非线性双曲型方程扩展混合有限元方法的误差估计

Abstract

Abstract:

In this paper, expanded mixed finite element method is developed for a class of nonlinear hyperbolic equation. A priori error estimate for the space discrete scheme is discussed in L^∞(L²) norm. Centered finite differences are used to advance in time, a fully discrete scheme is proposed. Further, a priori error estimate for the fully discrete scheme is established. Finally, a numerical example is presented to confirm the theoretical results.

Key words: Nonlinear hyperbolic equation, Expanded mixed finite element method, Error estimate

CLC Number:

O241.82

Keyan Wang,Qisheng Wang. Error Estimates for Expanded Mixed Finite Element Methods for Nonlinear Hyperbolic Equation[J].Acta mathematica scientia,Series A, 2021, 41(2): 468-478.

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Figures/Tables 2

References 15

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h	$\\|u-u_h\\|$	Rate	$\\|\mathit{\boldsymbol{ \widetilde{p}} }-\mathit{\boldsymbol{ \widetilde{p}} }_h\\|$	Rate	$\\|\mathit{\boldsymbol{p} }-\mathit{\boldsymbol{ p}} _h\\|$	Rate
1/4	3.0894e-2	-	9.2725e-1	-	9.5987e-1	-
1/8	8.2781e-3	1.90	2.4845e-1	1.90	2.5898e-1	1.89
1/16	2.1875e-3	1.92	6.6111e-2	1.91	6.9392e-2	1.90
1/32	5.8207e-4	1.91	1.7591e-2	1.91	1.8593e-2	1.90
1/64	1.5489e-4	1.91	4.6810e-3	1.91	4.9475e-3	1.91

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Error Estimates for Expanded Mixed Finite Element Methods for Nonlinear Hyperbolic Equation

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