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On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes

✍ Scribed by Abdellatif Agouzal; Konstantin Lipnikov; Yuri V. Vassilevski

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
797 KB
Volume
81
Category
Article
ISSN
0378-4754

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✦ Synopsis

We describe a new method for generating meshes that minimize the gradient of a discretization error. The key element of this method is construction of a tensor metric from edge-based error estimates. In our papers [1][2][3][4] we applied this metric for generating meshes that minimize the gradient of P 1 -interpolation error and proved that for a mesh with N triangles, the L 2 -norm of gradient of the interpolation error is proportional to N -1/2 . In the present paper we recover the tensor metric using hierarchical a posteriori error estimates. Optimal reduction of the discretization error on a sequence of adaptive meshes will be illustrated numerically for boundary value problems ranging from a linear isotropic diffusion equation to a nonlinear transonic potential equation.

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