Mesh generation and numerical analysis of a Galerkin method for highly conductive prefractal layers (Q1936177)

The authors provide a piecewise linear Galerkin approximation of a second order transmission problem across a highly conductive prefractal layer of von Koch type. An appropriate mesh adapted to the geometric shape of the interface is firstly generated and then a refinement algorithm consistent with a suitable estimate in appropriate weighted Sobolev spaces is constructed. A quasi-optimal error estimate in the energy norm is also obtained. Some numerical tests are presented to demonstrate the validity of the theory.