A finite element method for domain decomposition with non-matching grids
TLDR
In this paper, a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions is presented.Abstract:
In this note, we propose and analyse a method for handling interfaces between non-matching grids based on an approach suggested by Nitsche (1971) for the approximation of Dirichlet boundary conditions. The exposition is limited to self-adjoint elliptic problems, using Poisson's equation as a model. A priori and a posteriori error estimates are given. Some numerical results are included.read more
Citations
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Journal ArticleDOI
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
TL;DR: In this paper, a framework for the analysis of a large class of discontinuous Galerkin methods for second-order elliptic problems is provided, which allows for the understanding and comparison of most of the discontinuous methods that have been proposed over the past three decades.
Journal ArticleDOI
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
Paul Castillo,Bernardo Cockburn +1 more
TL;DR: This paper presents the first a priori error analysis for the local discontinuous Galerkin (LDG) method for a model elliptic problem and shows that, for stabilization parameters of order one, the L2-norm of the gradient and the L1- norm of the potential are of order k and k+1/2, respectively.
Journal ArticleDOI
Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method
Peter Hansbo,Mats G. Larson +1 more
TL;DR: A discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes is proposed and analyzed and optimal error estimates that are uniform with respect to Poisson's ratio are shown.
Book ChapterDOI
Discontinuous Galerkin Methods for Elliptic Problems
TL;DR: This work provides a common framework for the understanding, comparison, and analysis of several discontinuous Galerkin methods that have been proposed for the numerical treatment of elliptic problems.
Journal ArticleDOI
A discontinuous Galerkin method with nonoverlapping domain decomposition for the Stokes and Navier-Stokes problems
TL;DR: A family of discontinuous Galerkin finite element methods is formulated and analyzed for Stokes and Navier-Stokes problems and it is shown that the method can treat a finite number of nonoverlapping domains with nonmatching grids at interfaces.
References
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Book
Galerkin Finite Element Methods for Parabolic Problems
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
Journal ArticleDOI
An Interior Penalty Finite Element Method with Discontinuous Elements
TL;DR: In this paper, a semidiscrete finite element method for the solution of second order nonlinear parabolic boundary value problems is formulated and analyzed, where the test and trial spaces consist of discontinuous piecewise polynomial functions over quite general meshes with interelement continuity enforced approximately by means of penalties.
Journal ArticleDOI
Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind
Book
Finite elements in fluids
Richard H. Gallagher,T. J. Chung +1 more
TL;DR: In this paper, the Navier-Stokes Equations were used to model the flow of two Incompressible Non-miscible Viscous Fluids, and the Finite Element method was used to compute the flow.