Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities

Wang, Fei; Han, Weimin; Cheng, Xiaoliang

doi:10.1137/09075891x

Cited by 82 publications

(48 citation statements)

References 47 publications

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“…Both the energy norm and the L 2 norm of the error are studied, and the upper bound and the lower bound obtained illustrate that the analysis presented here is optimal. The RM element pretends to be one fit for fourth order elliptic perturbation problems, and can also expect application for contact/obstacle problems (c.f., e.g., [34,38]) in the future.…”

Section: Discussionmentioning

confidence: 99%

Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions

2016

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In this paper, we present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove that the convergence of the scheme is of O(h) order in energy norm and of O(h 2 ) order in L 2 norm on general d-rectangular triangulations. Moreover, when the triangulation is uniform, the convergence rate can be of O(h 2 ) order in energy norm, and the convergence rate in L 2 norm is still of O(h 2 ) order, which can not be improved. Numerical examples are presented to demonstrate our theoretical results.

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Section: Discussionmentioning

confidence: 99%

Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions

2016

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“…In [1,2], Arnold, Brezzi, Cockburn, and Marini provided a unified error analysis of DG methods for linear elliptic boundary value problems of second-order and succeeded in building a bridge between these two families of DG methods, establishing a framework to understand their properties, differences and the connections between them. In [21], numerous DG methods were extended for solving elliptic variational inequalities of second-order, and a priori error estimates were established, which are of optimal order for linear elements. DG methods for the Signorini problem and a quasistatic contact problem were also studied in [22,23], respectively.…”

Section: Discontinuous Galerkin Methodsmentioning

confidence: 99%

Discontinuous Galerkin Methods for an Elliptic Variational Inequality of Fourth-Order

Wang

Han

Huang

et al. 2015

Advances in Mechanics and Mathematics

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“…Of course, the situation here is slightly more involved because we are dealing with a saddle point problem, but it is conjectured that the arguments presented in [21] carry over to our problem.…”

Section: Define As Followsmentioning

confidence: 98%

Discontinuous Galerkin finite element discretization for steady Stokes flows with threshold slip boundary condition

Djoko

2013

Quaestiones Mathematicae

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Abstract. This work is concerned with the discontinuous Galerkin finite approximations for the steady Stokes equations driven by slip boundary condition of "friction" type. Assuming that the flow region is a bounded, convex domain with a regular boundary, we formulate the problem and its discontinuous Galerkin approximations as mixed variational inequalities of the second kind with primitive variables. The well posedness of the formulated problems are established by means of a generalization of the Babuska-Brezzi theory for mixed problems. Finally, a priori error estimates using energy norm for both the velocity and pressure are obtained. (2010): 65N30, 76D07, 35J85. Mathematics Subject Classification

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Discontinuous Galerkin Methods for Solving Elliptic Variational Inequalities

Cited by 82 publications

References 47 publications

Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions

Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions

Discontinuous Galerkin Methods for an Elliptic Variational Inequality of Fourth-Order

Discontinuous Galerkin finite element discretization for steady Stokes flows with threshold slip boundary condition

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