Optimal BV Estimates for a Discontinuous Galerkin Method for Linear Elasticity
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چکیده
Discontinuous Galerkin (DG) finite-element methods for secondand fourth-order elliptic problems were introduced about three decades ago. These methods stem from the hybrid methods developed by Pian and his coworker [25]. At the time of their introduction, DG methods were generally called interior penalty methods, and were considered by Baker [4], Douglas Jr. [14], and Douglas Jr. and Dupont [15] for fourth-order problems, where C continuity was imposed on C elements. For second-order equations, Nitsche [21] appears to have introduced the ideas of imposing Dirichlet boundary conditions weakly and of adding stabilization terms to obtain optimal convergence rates. The same idea of penalizing jumps along interelement faces led to the interior penalty methods of Percell and Wheeler [24] and Wheeler [30]. Methods for a second-order, nonlinear, parabolic equation appeared in [1]. According to [3], interest in DG methods for solving elliptic problems waned because they were never proven to be more advantageous than traditional conforming elements. The difficulty in identifying optimal penalty parameters and efficient solvers may also have contributed to the lack of interest [3]. Recently, however, interest has been rekindled by developments in DG methods for convection-diffusion problems; see, for example, Cockburn and Shu [12, 13], Oden, Babuška, and Baumann [22], Castillo, Cockburn,
منابع مشابه
Optimal Error Estimates for Discontinuous Galerkin Methods Applied to Linear Elasticity Problems
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تاریخ انتشار 2004