| 广义神经传播方程H~1-Galerkin低阶非协调混合有限元的超收敛分析 |
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| 作者单位： | ;1.河南城建学院数理学院;2.南阳师范学院数学与统计学院 |
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| 摘 要： | 利用EQrot和零阶R-T元对广义神经传播方程,建立了H1-Galerkin低阶非协调混合有限元的半离散格式.首先证明了逼近格式解的存在唯一性,然后利用EQrot元的特殊性质、零阶R-T元的高精度结果及插值后处理算子,导出了精确解u在H1模及中间变量p→在H(div;Ω)模意义下的超逼近性质和整体超收敛结果.
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| 关 键 词： | 广义神经传播方程 H1-Galerkin方法 低阶非协调混合元 半离散与全离散 |
Superconvergence Analysis of the Lowest Order H~1-Galerkin Nonconforming Mixed Finite Element for Generalized Nerve Conduction Type Equations |
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| Affiliation: | ,School of Mathematics and Physics,Henan University of Urban Constrution,School of Mathematics and Statistics,Nanyang Normal University |
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| Abstract: | By employing EQrot element and zero-order Raviart-Thomas element,H1-Galerkin nonconforming mixed finite element scheme was discussed for a class of generalized nerve conduction type equations under semi-discrete.The existence and uniqueness of the solution about the approximation scheme were proved.Based on the special characters of EQrot element,the known high accuracy analysis of zero-order R-T element and the post processing technique,the superclose and superconvergence properties for uin H1-norm and p→in H(div;Ω)-norm were obtained for the above scheme. |
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| Keywords: | generalized nerve conduction type equations H1-Galerkin method low order nonconforming mixed finite element superclose and superconvergence |
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