Abstract
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N h triangles, the error is proportional to \(N_h^{-1}\) and the gradient of error is proportional to \(N_h^{-1/2}\) which are the optimal asymptotics. The methodology is verified with numerical experiments.
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Agouzal, A., Lipnikov, K., Vassilevski, Y. (2009). Anisotropic Mesh Adaptation for Solution of Finite Element Problems Using Hierarchical Edge-Based Error Estimates. In: Clark, B.W. (eds) Proceedings of the 18th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04319-2_34
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DOI: https://doi.org/10.1007/978-3-642-04319-2_34
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