Two families of conforming finite elements for the two-dimensional Stokes problem are developed, guided by two discrete smoothed de Rham complexes, which we coin “Stokes complexes.” We show that the finite element pairs are inf-sup stable and also provide pointwise mass conservation on very general triangular meshes.

We present spectral methods for solving the Stokes problem in a circular domain. Their main feature is the uniform inf-sup condition, which allows for optimal error estimates. We apply them to the resolution of exterior problems by coupling with the transparent boundary condition.

We report on recent results related to domain decomposition methods based on the Discontinuous Galerkin discretizations of Stokes equations. We analyze the efficiency of a block nonoverlapping Schwarz preconditioner based on the approach by Feng and Karakashian [2001]. We also prove the inf-sup stability of a substructuring method.

The purpose of this paper is to present a rather simple proof of an inequality of Nečas [9] which is equivalent to the inf-sup condition. This inequality is fundamental in the study of the Stokes equations. The boundary of the domain is only assumed to be Lipschitz.

In this work, the rectangular nonconforming Wilson element in solving incompress-ible elastic equation is analyzed. Although the element does not satisses the inf-sup condition (in a mixed formulation), it still can be used to compute the displacement successfully. If a simple post-processing is applied, the pressure converges, too. An optimal convergence rate is established for both displaceme...

In this work we introduce a new a posteriori error estimate of hierarchical type for the advection-diffusion-reaction equation. We prove the equivalence between the energy norm of the error and our error estimate using an auxiliary linear problem for the residual and an easy way to prove inf–sup condition.

The purpose of this study was to quantify regional variations in material properties of the glenohumeral joint posterior capsule and to compare these data with the anterior band of the inferior glenohumeral ligament (AB-IGHL). Mechanical properties were determined for individual bands of the AB-IGHL, superior posterior capsule (SUP-PC), middle posterior capsule (MID-PC), and inferior posterior ...

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous Pr−1-elements for the pressure where the order r can vary from element to element between 2 and a fixed bound r∗. We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes ...

In this paper, we propose an efficient proper orthogonal decomposition based reduced-order model(POD-ROM) for nonstationary Stokes equations, which combines the classical projection method with POD technique. This new scheme mainly owns two advantages: first one is low computational costs since decouples velocity variable and pressure variable, technique further improves efficiency; second adva...