J4 ›› 2011, Vol. 46 ›› Issue (4): 23-28.
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郑瑞瑞,孙同军
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作者简介:
基金资助:
山东省中青年科学家奖励基金(BS2009NJ003)
ZHENG Rui-rui, SUN Tong-jun
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摘要：
在有限元空间上采用迎风混合元方法对线性Sobolev方程进行数值模拟。此方法对线性Sobolev方程中的对流项采用迎风格式处理,扩散项则采用扩展的混合元来逼近, 降低了对解空间光滑度的要求,能同时高精度地对未知纯量以及流量进行估计,得到最优的L2-模误差估计。最后,数值例子将进一步说明该方法的可行性和有效性。
关键词: 迎风混合元方法；线性Sobolev方程；最优误差估计
Abstract:
An upwind-mixed method is presented to simulate the linear Sobolev equation in finite element space. The convection term in the linear Sobolev equation is approximated by the upwind method and the diffusion term by an expanded mixed finite element method. The method can simultaneously approximate the scalar unknown and the vector flux effectively, reducing the continuity of the finite element space. Optimal rate error estimates in L2-norm can be obtained. Finally, numerical experiment is given to illustrate the efficiency of the method.
Key words: upwind-mixed method; linear Sobolev equation; optimal error estimates
郑瑞瑞,孙同军. 一类线性Sobolev方程的迎风混合元方法[J]. J4, 2011, 46(4): 23-28.
ZHENG Rui-rui, SUN Tong-jun. An upwind-mixed method for the linear Sobolev equation[J]. J4, 2011, 46(4): 23-28.
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