Another Attempt to Overcome the Bent Element Blues

摘要

This paper is the second of a pair in which we attempt, mostly unsuccessfully, to patch a perceived defect in the Galerkin finite element approximations to the pressure gradient. The first was presented earlier this year (Gresho, et al. (1984a)). specifically, we address the problems associated with the bilinear velocity, piecewise-constant pressure element for solving the incompressible Navier-Stokes equations. When the discrete approximation to gradient of P is examined on a mesh of distorted elements (via the bilinear isoparametric mapping), it appears to be not very accurate; from a Taylor series viewpoint, this element is not meant to be bent. After exposing these alleged defects, we proceed to patch the gradient approximation. In the limited context of our techniques used to integrate the time-dependent equations, we discuss and demonstrate the advantages of the new approximation. But we also discuss the numerous disadvantages uncovered during our investigation and, in the end, admit failure - and we continue to sing the Bent Element Blues. (ERA citation 09:025125)