Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
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DOI：
10.1137/120871821
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发表时间：
2012-07
期刊：
影响因子：
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通讯作者：
Buyang Li;Weiwei Sun
中科院分区：
文献类型：
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作者：
Buyang Li;Weiwei Sun
本文研究了多孔介质中不可压缩混溶流方程的Galerkin混合有限元线性化半隐式Euler格式的无条件收敛性和误差估计。我们证明了最优L^2 $误差估计在没有任何时间步长（收敛）条件下成立，而以前的所有工作都需要一定的时间步长限制。我们的理论结果提供了一个新的理解常用的线性格式。证明是基于分裂的误差分为两部分：从时间离散的偏微分方程的误差和相应的时间离散偏微分方程的有限元离散的误差。本文所用的方法可以应用于更一般的非线性抛物型方程组和许多其他线性化（半）隐式时间离散。
In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal $L^2$ error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Our theoretical results provide a new understanding on commonly used linearized schemes. The proof is based on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of corresponding time-discrete PDEs. The approach used in this paper can be applied to more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations.