论文标题
使用连续内部惩罚的有限元离职
Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty
论文作者
论文摘要
我们考虑了具有对称稳定的有限元方法，用于离散瞬态对流方程。对于时间限制，我们考虑二阶向后分化公式或曲柄 - 尼科尔森方法。对流项和相关的稳定都使用推断的近似解决方案明确处理。我们证明了该方法的稳定性和$τ^2 + h^{p + {\ frac12}} $ $ l^2 $ - norm的错误估计在标准双波利的CFL条件下，当使用分段（$ p = 1 $）近似值时，或者在使用有限级元素的情况下，或者在有限元中$ p \ p p \ p pe p \ ge 1 cort \ ge 1 corter $ pe \ ge 1，即$τ\ leq c h^{4/3} $。该理论用一些数值示例进行了说明。
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or the Crank-Nicolson method. Both the convection term and the associated stabilisation are treated explicitly using an extrapolated approximate solution. We prove stability of the method and the $τ^2 + h^{p+{\frac12}}$ error estimates for the $L^2$-norm under either the standard hyperbolic CFL condition, when piecewise affine ($p=1$) approximation is used, or in the case of finite element approximation of order $p \ge 1$, a stronger, so-called $4/3$-CFL, i.e. $τ\leq C h^{4/3}$. The theory is illustrated with some numerical examples.
