| AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO—HYPERBOLIC EQUATIONS |
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| 作者姓名： | XiaCui |
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| 作者单位： | LaboratoryofComputationalphysics,InstituleofAppliedPhysicsandComputationalMathematics,P.O.Box8009-26,Beijing100088,China |
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| 基金项目： | Supported by China National Key Program for Developing Basic Sciences (G1999032801)，Mathematical Tianyuan Foundation (10226026) and NNSF of China (19932010). |
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| 摘 要： | AD(Alternating direction)Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied.By using patch approximation technique,AD procedure is realized,and calculation,work is simplified.By using Galerkin approach,highly computational accuracy is kept.By using various priori estimate techniques for differential equations,difficulty coming form non-linearity is treated,and optimal H^1 and L^2 convergence prop-erties are demonstrated.Moreover,although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment,yet the schemes formulated in this paper have second order accuracy in it.This implies an essential advancement in AD Galerkin aualysis.
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| 关 键 词： | 交替方向伽辽金格式 非线性伪双曲方程 AD 路径近似 优先估计 精确度 |
AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS |
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| XiaCui.AD GALERKIN ANALYSIS FOR NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS[J].Journal of Computational Mathematics,2003,21(2):125-134. |
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| Authors: | Xia Cui |
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| Abstract: | AD (Alternating direction) Galerkin schemes for d-dimensional nonlinear pseudo-hyperbolic equations are studied. By using patch approximation technique, AD procedure is realized, and calculation work is simplified. By using Galerkin approach, highly computational accuracy is kept. By using various priori estimate techniques for differential equations, difficulty coming from non-linearity is treated, and optimal H1 and L2 convergence properties are demonstrated. Moreover, although all the existed AD Galerkin schemes using patch approximation are limited to have only one order accuracy in time increment, yet the schemes formulated in this paper have second order accuracy in it. This implies an essential advancement in AD Galerkin analysis. |
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| Keywords: | nonlinear pseudo-hyperbolic equation alternating direction numerical analy- sis |
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