Journal of Computational Physics
Stable finite elements for problems with wild coefficients
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
A hybrid method for moving interface problems with application to the Hele-Shaw flow
Journal of Computational Physics
Journal of Scientific Computing
Analysis of a nonoverlapping domain decomposition method for elliptic partial differential equations
Journal of Computational and Applied Mathematics
Analysis of non-overlapping domain decomposition algorithms with inexact solves
Mathematics of Computation
Some Nonoverlapping Domain Decomposition Methods
SIAM Review
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Lavrentiev Regularization + Ritz Approximation = Uniform Finite Element Error Estimates for Differential Equations with Rough Coefficients
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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.