Consistent SUPG-method for transient transport problems: Stability and convergence
Consistent SUPG-method for transient transport problems: Stability and convergence
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DOI：
10.1016/j.cma.2009.11.023
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发表时间：
2010-01-01
影响因子：
7.2
通讯作者：
Burman, Erik
中科院分区：
文献类型：
--
作者：
Burman, Erik
我们考虑瞬态对流方程的时间/空间离散化。空间离散采用流线迎风格式的彼得罗夫 - 伽辽金方法，时间离散则使用A - 稳定的有限差分算子。在稳定项中包含时间导数的意义下，该公式是强相容的。在数据满足正则性条件，或者满足允许离散化参数最优选择的适度逆库朗 - 弗里德里希斯 - 列维（CFL）条件下，证明了一般公式的一致稳定性。向后欧拉方法（BDF1）、克兰克 - 尼科尔森格式以及二阶向后差分公式（BDF2）都适用于该框架，并且证明了这些格式具有拟最优收敛性。© 2009爱思唯尔有限公司。保留所有权利。
We consider the time/space discretization of the transient advection equation. Discretization in space is performed by the streamline upwind Petrov-Galerkin method and in time we use an A-stable finite difference operator. The formulation is strongly consistent in the sense that the time derivative is included in the stabilization term. Uniform stability of the general formulation is proved under a regularity condition on data, or a moderate inverse CFL-condition that allows for optimal choices of the discretization parameters. Both the backward Euler method (BDF1), the Crank-Nicolson scheme and the second-order backward differentiation formula (BDF2) enter the framework and quasi-optimal convergence is proved for these schemes. (c) 2009 Elsevier B.V. All rights reserved.