Article ID Journal Published Year Pages File Type
499362 Computer Methods in Applied Mechanics and Engineering 2008 18 Pages PDF
Abstract

The goal of this paper is to motivate, introduce and demonstrate a novel approach to stabilizing discontinuous Galerkin (DG) methods in nonlinear elasticity problems. The stabilization term adapts to the solution of the problem by locally changing the size of a penalty term on the appearance of discontinuities, with the goal of better approximating the solution. Consequently, it is called an adaptive stabilization strategy. The need for such a strategy is motivated through two- and three-dimensional examples in nonlinear elasticity. The proposed scheme is simple to implement and compute, and its performance is demonstrated with two- and three-dimensional numerical examples. The accuracy of the proposed method is compared against a conforming method of the same order and a DG method with a traditional form of stabilization. Results for trilinear hexahedral elements indicate that the new stabilization strategy is more robust and more accurate when compared to a traditional form of stabilization. However, conforming trilinear hexahedral elements proved to be more computationally efficient for the examples shown here. A two-dimensional example with linear triangular elements showed comparable performances between the proposed method and a conforming one.

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Physical Sciences and Engineering Computer Science Computer Science Applications
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