Efficient numerical solution of one‐phase linear inverse Stefan and Cauchy–Stefan problems in two dimensions: A posteriori error control

Abstract

AbstractThe efficient numerical solution of the one‐phase linear inverse Stefan and Cauchy–Stefan problems is a delicate task owing to the problems' susceptibility to the perturbation of the given data. In this context, heuristic a posteriori error indicators are constructed for such inverse problems with noisy data in two dimensions (2D). Given a fixed computational effort, the estimator controls the error due to discretization by the method of fundamental solution (MFS). It is accomplished through two mean‐driven double‐filtering algorithms. Numerical results substantiate the effectiveness of the algorithms.