Finite elements for elliptic problems with wild coefficients

An iterative finite element algorithm is proposed for numerically solving interface problems with strongly discontinuous coefficients. This algorithm employs finite element methods and iteratively solves smaller subproblems with good accuracy, and exchanges information at the interface to advance the iteration until convergence, following the idea of the Schwarz Alternating Method. Numerical experiments are performed to show the accuracy and efficiency of the algorithm for capturing strong discontinuities in the coefficients. They show that the accuracy of our method does not deteriorate and it converges faster as the discontinuity in the coefficients becomes worse. Numerical comparisons are made for coefficient discontinuity jumps in the order of 0, 105, 1010, 1050, and 10100.