新的投影混合稳定化方法在抛物问题中的应用

A New Projection-type Mixed Stabilization for the Parabolic Problem

针对抛物问题提出一种新的投影混合稳定化方法.该方法基于等阶的混合有限元,相比通常的局部投影稳定化方法,增加了新的投影稳定项及压力跳跃项,有效地克服了等阶有限元不满足inf-sup条件而导致的解的不稳定性,也保证了该方法不仅对连续的压力空间适用,且对不连续的压力空间亦适用.本文证明了该方法的稳定性,并给出了误差估计.最后,数值算例验证了该方法的理论分析及有效性.

A new projection-type stabilized formulation for the parabolic problem is pro- posed. The method is based on the same equal-order mixed finite element space for both re- gions. Compared with usual local projection stabilization methods, we add a new projection- type stabilization term and a pressure jump term, which can effectively bypass the inf-sup condition. It also ensures that our technique can be applied to not only continuous pressure space but also discontinuous pressure space. The stability of the proposed scheme is proved. Error estimates are obtained. At last, some numerical experiments are given to verify our theoretical results and the efficiency.