## $$hp$$-anisotropic mesh adaptation technique based on interpolation error estimates.(English)Zbl 1340.65285

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, May 15–17, 2013. In honor of the 70th birthday of Karel Segeth. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-61-5). 32-41 (2013).
Summary: We present a completely new $$hp$$-anisotropic mesh adaptation technique for the numerical solution of partial differential equations with the aid of a discontinuous piecewise polynomial approximation. This approach generates general anisotropic triangular grids and the corresponding degrees of polynomial approximation based on the minimization of the interpolation error. We develop the theoretical background of this approach and present a numerical example demonstrating the efficiency of this anisotropic strategy in comparison with an isotropic one.
For the entire collection see [Zbl 1277.00032].

### MSC:

 65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65N15 Error bounds for boundary value problems involving PDEs
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