Abstract
The article presents analysis of a new methodology for generating meshes minimizing L p -norms of the interpolation error or its gradient, p > 0. The key element of the methodology is the construction of a metric from node-based and edge-based values of a given function. For a mesh with N h triangles, we demonstrate numerically that L ∞-norm of the interpolation error is proportional to N −1 and L ∞-norm of the gradient of the interpolation error is proportional to N −1/2 . The methodology can be applied to adaptive solution of PDEs provided that edge-based a posteriori error estimates are available.
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