双曲型积分微分方程H~1-Galerkin混合元法的误差估计

本文用H1-Galerkin混合有限元法分析了基于带有记忆项的多孔介质中的对流问题的数学模型,即双曲型积分微分方程．我们得到了在一维情况下函数和它梯度的最优阶误差估计, 并且由此推广到二维和三维情况下,得到了和用传统的混合元方法相同的收敛阶数,而且不用验证满足LBB相容性条件．

ERROR ESTIMATES FOR H1-GALERKIN MIXED FINITE ELEMENT METHODS FOR HYPERBOLIC TYPE INTEGRO-DIFFERENTIAL EQUATION

H1-Galerkin mixed finite element methods are analysed for hyperbolic partial integro-differential equations which arise in mathematical models of reactive flows in porous media and of materials with memory effects.Depending on the physical quantities of interest, two methods are discussed.Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension.An extension to problems in two and three space variables is also discussed and it is shown that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical methods without requiring the LBB consistency condition.