Maximum Norm Resolvent Estimates for Elliptic Finite Element Operators |
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Authors: | Nikolai Yu. Bakaev |
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Affiliation: | (1) Department of Mathematics, Air Force Technical University, Planetnaya St., 3, Moscow, 125190, Russia |
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Abstract: | We study a finite element approximation Ah, based on simplicial Lagrange elements, of a second order elliptic operator A under homogeneous Dirichlet boundary conditions in two and three dimensions, where h is thought of as a meshsize. The main result of the paper is a new resolvent estimate for the operator Ah in the L-norm. This estimate is uniform with respect to h for the case with at least quadratic elements. In the case with linear elements, the estimate contains on the right a factor proportional to (log log ), where = 1 or = in two or three dimensions, respectively.This revised version was published online in October 2005 with corrections to the Cover Date. |
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Keywords: | Elliptic operator finite element approximation resolvent estimate |
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