On the initial higher-order pressure convergence in equal-order finite element discretizations of the Stokes system
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3052242Utgivelsesdato
2022Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2527]
- Publikasjoner fra CRIStin - NTNU [38679]
Originalversjon
10.1016/j.camwa.2022.01.022Sammendrag
In incompressible flow problems, the finite element discretization of pressure and velocity can be done through either stable spaces or stabilized pairs. For equal-order stabilized methods with piecewise linear discretization, the classical theory guarantees only linear convergence for the pressure approximation. However, a higher order is often observed, yet seldom discussed, in numerical practice. Such experimental observations may, in the absence of a sound a priori error analysis, mislead the selection of finite element spaces in practical applications. Therefore, we present here a numerical analysis demonstrating that an initial higher-order pressure convergence may in fact occur under certain conditions, for equal-order elements of any degree. Moreover, our numerical experiments clearly indicate that whether and for how long this behavior holds is a problem-dependent matter. These findings confirm that an optimal pressure convergence can in general not be expected when using unbalanced velocity-pressure pairs.