Convergence analysis of enhanced Phragmén–Lindelöf methods for solving elliptic Dirichlet problems

Abstract

In this paper, we explore the ball convergence properties of enhanced Phragmén–Lindelöf type methods for solving the Dirichlet problem with an elliptic operator. By placing requirements on the elliptic operator and auxiliary points, we characterize the ball limit of a series of elliptic operators in non‐divergence form. Considering all dimensions, it becomes apparent that dealing solely with measurable and bounded coefficients for this class of operators is insufficient, necessitating additional regularity assumptions on them. We find the radii of convergence balls using recurrence relations, so as to guarantee the convergence of iterative reconstruction techniques, beginning from any point inside the ball centered on an auxiliary point.