Nested Newton strategies for energy-corrected finite element methods (Q6486736)

The authors consider the energy-corrected finite element methods to approximate elliptic problems in domains with re-entrant corners. One of the important questions is how to determine the optimal correction factors in practice. In the present work, it is shown that asymptotically a unique correction parameter exists and that it can be formally obtained as the limit of level dependent correction parameters which are defined as roots of an energy defect function. In addition to this, three nested Newton-type algorithms are proposed using only one Newton step per refinement level and local (or even) global convergence to this asymptotic correction parameter is shown.