Precise FEM solution of a corner singularity using an adjusted mesh

TLDR: In this article, the authors present an alternative approach for flow problems on domains with corner singularities, using the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner.

Abstract: Within the framework of the finite element method problems with corner-like singularities (e.g. on the well-known L-shaped domain) are most often solved by the adaptive strategy: the mesh near the corners is refined according to the a posteriori error estimates. In this paper we present an alternative approach. For flow problems on domains with corner singularities we use the a priori error estimates and asymptotic expansion of the solution to derive an algorithm for refining the mesh near the corner. It gives very precise solution in a cheap way. We present some numerical results. Copyright © 2005 John Wiley & Sons, Ltd.

Figures

Fig. 5: Streamlines 0.0295 0.03 0.0305

Fig. 9: Errors on elements - whole refined area

Fig. 1: Geometry of the channel

Fig. 11: Errors on elements - with smallest elements

Fig. 2: Refined detail of mesh

Fig. 10: Errors on elements - detail

Frequently asked questions

Q1. What are the contributions in "Precise fem solution of corner singularity using adjusted mesh applied to 2d flow" ?

The authors present an alternative approach to the adaptive mesh refinement. For steady Navier-Stokes equations the authors proved in [ 1 ] that for nonconvex internal angles the velocities near the corners possess an expansion u ( ρ, θ ) = ρφ ( θ ) +... ( + smoother terms ), where ρ, θ are local spherical coordinates. The authors show an example of 2D mesh with quadratic polynomials for velocity.