Low-order dPG-FEM for an elliptic PDE

C. Carstensen; D. Gallistl; F. Hellwig; L. Weggler

doi:10.1016/j.camwa.2014.09.013

Low-order dPG-FEM for an elliptic PDE

C. Carstensen, D. Gallistl, F. Hellwig, L. Weggler

Research output: Contribution to journal › Article › Academic › peer-review

11 Citations (Scopus)

Abstract

This paper introduces a novel lowest-order discontinuous Petrov–Galerkin (dPG) finite element method (FEM) for the Poisson model problem. The ultra-weak formulation allows for piecewise constant and affine ansatz functions and for piecewise affine and lowest-order Raviart–Thomas test functions. This lowest-order discretization for the Poisson model problem allows for a direct proof of the discrete inf–sup condition and a complete a priori and a posteriori error analysis. Numerical experiments investigate the performance of the method and underline the quasi-optimal convergence.

Original language	English
Pages (from-to)	1503-1512
Number of pages	10
Journal	Computers and mathematics with applications
Volume	68
Issue number	11
DOIs	https://doi.org/10.1016/j.camwa.2014.09.013
Publication status	Published - 2014
Externally published	Yes

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Carstensen, C., Gallistl, D., Hellwig, F., & Weggler, L. (2014). Low-order dPG-FEM for an elliptic PDE. Computers and mathematics with applications, 68(11), 1503-1512. https://doi.org/10.1016/j.camwa.2014.09.013

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AU - Gallistl, D.

AU - Hellwig, F.

AU - Weggler, L.

PY - 2014

Y1 - 2014

N2 - This paper introduces a novel lowest-order discontinuous Petrov–Galerkin (dPG) finite element method (FEM) for the Poisson model problem. The ultra-weak formulation allows for piecewise constant and affine ansatz functions and for piecewise affine and lowest-order Raviart–Thomas test functions. This lowest-order discretization for the Poisson model problem allows for a direct proof of the discrete inf–sup condition and a complete a priori and a posteriori error analysis. Numerical experiments investigate the performance of the method and underline the quasi-optimal convergence.

AB - This paper introduces a novel lowest-order discontinuous Petrov–Galerkin (dPG) finite element method (FEM) for the Poisson model problem. The ultra-weak formulation allows for piecewise constant and affine ansatz functions and for piecewise affine and lowest-order Raviart–Thomas test functions. This lowest-order discretization for the Poisson model problem allows for a direct proof of the discrete inf–sup condition and a complete a priori and a posteriori error analysis. Numerical experiments investigate the performance of the method and underline the quasi-optimal convergence.

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DO - 10.1016/j.camwa.2014.09.013

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