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Full-Text Articles in Physical Sciences and Mathematics
Natural Superconvergent Points Of Triangular Finite Elements, Zhimin Zhang, Runchang Lin
Natural Superconvergent Points Of Triangular Finite Elements, Zhimin Zhang, Runchang Lin
Mathematics Research Reports
In this work, we analytically identify natural superconvergent points of function values and gradients for triangular elements. Both the Poisson equation and the Laplace equation are discussed for polynomial finite element spaces (with degrees up to 8) under four different mesh patterns. Our results verify computer findings of [2], especially, we confirm that the computed data have 9 digits of accuracy with an exception of one pair (which has 8-7 digits of accuracy). In addition, we demonstrate that the function value superconvergent points predicted by the symmetry theory [14] are the only superconvergent points for the Poisson equation. Finally, we …
Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan
Impulse Control Of Stochastic Navier-Stokes Equations, J. L. Menaldi, S. S. Sritharan
Mathematics Faculty Research Publications
In this paper we study stopping time and impulse control problems for stochastic Navier-Stokes equation. Exploiting a local monotonicity property of the nonlinearity, we establish existence and uniqueness of strong solutions in two dimensions which gives a Markov-Feller process. The variational inequality associated with the stopping time problem and the quasi-variational inequality associated with the impulse control problem are resolved in a weak sense, using semigroup approach with a convergence uniform over path.