Error indicators based on solution gradients, interpolation errors, and a posteriori error estimates are presented for use in defining monitor functions for the r-adaptive finite element methods based on moving mesh partial differential equations. The methods are compared with a careful...

In this paper, we develop a finite element model for a cable suspended in water. Global existence and uniqueness of solutions of the truncated system is shown for a slightly simplified equation describing the motion of a cable having negligible added mass and supported by fixed end-points. Based...

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...

In this paper use is made of the superconvergence property of the recovered derivatives of piecewise linear finite element solutions of Poisson problems to construct efficient and simple to use error estimators which have the desired property of being asymptotically exact on structured...