Agouzal, A.; Lipnikov, K.; Vassilevski, Yu. 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. Cited in 1 ReviewCited in 7 Documents MSC: 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs Keywords:optimal mesh; interpolation error; metric based adaptation; mesh generation; a posteriori error estimates PDFBibTeX XMLCite \textit{A. Agouzal} et al., Zh. Vychisl. Mat. Mat. Fiz. 50, No. 1, 131--145 (2010; Zbl 1224.65283) Full Text: DOI