Anisotropic hp-adaptive method based on interpolation error estimates in the L-q-norm

• ID: 2662, RIV: 10272215
• ISSN: 0168-9274, ISBN: not specified
• source: Applied Numerical Mathematics
• keywords: Anisotropic hp-adaptive method; interpolation error estimates;
• authors: Vít Dolejší
• authors from KNM: Dolejší Vít

Abstract

We present a new anisotropic $hp$-adaptive technique, which can be employed for the numerical solution of various scientific and engineering problems governed by partial differential equations in 2D with the aid of a discontinuous piecewise polynomial approximation. This method generates anisotropic triangular grids and the corresponding polynomial approximation degrees based on the minimization of the interpolation error in the $L^q$-norm. We develop the theoretical background of this approach and present several numerical examples demonstrating the efficiency of the anisotropic adaptive strategy.