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Hessian-free metric-based mesh adaptation via geometry of interpolation error. (English) Zbl 1224.65283

Zh. Vychisl. Mat. Mat. Fiz. 50, No. 1, 131-145 (2010) and Comput. Math., Math. Phys. 50, No. 1, 124-138 (2010).
Summary: The article presents analysis of a new methodology for generating meshes minimizing \(L^p\)-norms, \(p > 0\), of the interpolation error or its gradient. 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 \(L^{\infty}\)-norm of the interpolation error is proportional to \(N_h^{-1}\) and \(L^{\infty}\)-norm of the gradient of the interpolation error is proportional to \(N_h^{-1/2}\). The methodology can be applied to adaptive solution of partial differential equations provided that edge-based a posteriori error estimates are available.

MSC:

65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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