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   Checkerboard Error Eliminated by Mesh Adaptation:
Figure 5.24 shows the Cp contours of a flow over a Jukowsky airfoil computed by a least-squares finite-element scheme for the Cauchy-Riemann system of velocities. A typical checkerboard error can be seen. The scheme is based on the residual over the quadrilateral element with solution values stored at nodes; such a scheme is suseptible to the checkerboard error (a high-frequency mode is transparent to such a residual).

Figure 5.26 below shows the Cp contours obtained by mesh adaptation: nodes were moved to minimize the residuals simultaneously computing the solution. It converged rapidly, resulting in a mesh with checkerboard pertubation. Implication is that a bad mesh can be a good mesh for a bad scheme.

See [ PhD Thesis ], Section 5.2.5, page 115, for more details.
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Copyright 1994- by Hiroaki Nishikawa. All rights reserved.