A Mesh Optimization Algorithm To Decrease The Maximum Error In Finite Element Computations

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 W-1,W-infinity semi-norm of the interpolation error. For these examples, the L-2, L-infinity, and H-1 norms decreased also.