Mesh generation and numerical analysis of a Galerkin method for highly conductive prefractal layers

In this paper we provide a piecewise linear Galerkin approximation of a second order transmission problem across a highly conductive prefractal layer of von Koch type. We firstly generate an appropriate mesh adapted to the geometric shape of the interface and then we construct a refinement algorithm consistent with a suitable estimate in appropriate weighted Sobolev spaces. We also obtain a quasi-optimal error estimate in the energy norm and finally we demonstrate the validity of our theory through numerical tests. © 2012 IMACS.

Published in:
Applied Numerical Mathematics, 65, 63-78

 Record created 2017-04-03, last modified 2018-09-13

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