DCDS-B
Stabilized finite element method for the non-stationary Navier-Stokes problem
Yinnian He Yanping Lin Weiwei Sun
In this article, a locally stabilized finite element formulation of the two-dimensional Navier-Stokes problem is used. A macroelement condition which provides the stability of the $Q_1-P_0$ quadrilateral element and the $P_1-P_0$ triangular element is introduced. Moreover, the $H^1$ and $L^2$-error estimates of optimal order for finite element solution $(u_h,p_h)$ are analyzed. Finally, a uniform $H^1$ and $L^2$-error estimates of optimal order for finite element solution $(u_h,p_h)$ is obtained if the uniqueness condition is satisfied.
keywords: stabilized finite element uniform error estimate. Navier-Stokes problem
DCDS-B
Error estimation of a class of quadratic immersed finite element methods for elliptic interface problems
Tao Lin Yanping Lin Weiwei Sun
We carry out error estimation of a class of immersed finite element (IFE) methods for elliptic interface problems with both perfect and imperfect interface jump conditions. A key feature of these methods is that their partitions can be independent of the location of the interface. These quadratic IFE spaces reduce to the standard quadratic finite element space when the interface is not in the interior of any element. More importantly, we demonstrate that these IFE spaces have the optimal (slightly lower order in one case) approximation capability expected from a finite element space using quadratic polynomials.
keywords: interface error estimates. immersed finite element method Elliptic jump condition

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