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

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  • Agouzal, Abdellatif
  • Lipnikov, Konstantin
  • Vassilevski, Yuri V.

Abstract

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 [1–4] we applied this metric for generating meshes that minimize the gradient of P1-interpolation error and proved that for a mesh with N triangles, the L2-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.

Suggested Citation

  • Agouzal, Abdellatif & Lipnikov, Konstantin & Vassilevski, Yuri V., 2011. "On optimal convergence rate of finite element solutions of boundary value problems on adaptive anisotropic meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 1949-1961.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:10:p:1949-1961
    DOI: 10.1016/j.matcom.2010.12.027
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