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A mesh optimization algorithm to decrease the maximum error in finite element computations

Hetmaniuk, U.; Knupp, Patrick K.

We present a mesh optimization algorithm for adaptively improving the finite element interpolation of a function of interest. The algorithm minimizes an objective function by swapping edges and moving nodes. Numerical experiments are performed on model problems. The results illustrate that the mesh optimization algorithm can reduce the W1,āˆž semi-norm of the interpolation error. For these examples, the L2, Lāˆž, and H1 norms decreased also.