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Results 1 - 10
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333
Unified analysis of discontinuous Galerkin methods for elliptic problems
- SIAM J. Numer. Anal
, 2001
"... Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment ..."
Abstract
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Cited by 525 (31 self)
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Abstract. We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical
UNIFIED HYBRIDIZATION OF DISCONTINUOUS GALERKIN, MIXED AND CONTINUOUS GALERKIN METHODS FOR SECOND ORDER ELLIPTIC PROBLEMS
"... Abstract. We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continuous Galerkin, non-conforming and a new wide cla ..."
Abstract
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Cited by 100 (18 self)
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Abstract. We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continuous Galerkin, non-conforming and a new wide
Weak Galerkin methods for second order elliptic interfaces. preprint arXiv:1201.6438
"... Abstract. Weak Galerkin methods refer to general finite element methods for partial differ-ential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and inter-face conditio ..."
Abstract
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Cited by 6 (2 self)
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conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. The paper also presents many numerical tests for validating the WG-FEM for solving second order elliptic interface problems. For such interface
Low order discontinuous Galerkin methods for second order elliptic problems
- SIAM J. Numer. Anal
"... Abstract. We consider DG-methods for 2nd order scalar elliptic problems using piecewise affine approximation in two or three space dimensions. We prove that both the symmetric and the nonsymmetric version of the DG-method are well-posed also without penalization of the interelement solution jumps pr ..."
Abstract
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Cited by 10 (3 self)
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conservation. AMS subject classifications. 65M160, 65M15 1. Introduction. The discontinuous Galerkin method (DG) for (2n)th-order elliptic problems was introduced and analysed by Baker [2] with special focus on the fourth order case. In this work both the jumps of the solution and its gradient were
A Discontinuous Petrov-Galerkin method with Lagrangian multipliers for second order elliptic problems
- SIAM J. NUMER. ANAL
"... We present a Discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG)) whi ..."
Abstract
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Cited by 4 (1 self)
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We present a Discontinuous Petrov-Galerkin method (DPG) for finite element discretization scheme of second order elliptic boundary value problems. The novel approach emanates from a one-element weak formulation of the differential problem (that is typical of Discontinuous Galerkin methods (DG
A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
- Math. Comp
"... Abstract. We identify and study an LDG-hybridizable Galerkin method, which is not an LDGmethod, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuousGalerkinmethods using polynomials of degree k ≥ 0 for both the po ..."
Abstract
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Cited by 37 (10 self)
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Abstract. We identify and study an LDG-hybridizable Galerkin method, which is not an LDGmethod, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuousGalerkinmethods using polynomials of degree k ≥ 0 for both
SUPERCONVERGENT DISCONTINUOUS GALERKIN METHODS FOR SECOND-ORDER ELLIPTIC PROBLEMS
"... Abstract. We identify discontinuous Galerkin methods for second-order elliptic problems in several space dimensions having superconvergence properties similar to those of the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods. These methods use polynomials of degree k ≥ 0 for both the potent ..."
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Cited by 30 (9 self)
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Abstract. We identify discontinuous Galerkin methods for second-order elliptic problems in several space dimensions having superconvergence properties similar to those of the Raviart-Thomas and the Brezzi-Douglas-Marini mixed methods. These methods use polynomials of degree k ≥ 0 for both
Results 1 - 10
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333
