Low-order dPG-FEM for an elliptic PDE

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

Research output: Contribution to journalArticleAcademicpeer-review

10 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 languageEnglish
Pages (from-to)1503-1512
Number of pages10
JournalComputers and mathematics with applications
Volume68
Issue number11
DOIs
Publication statusPublished - 2014
Externally publishedYes

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Petrov-Galerkin Method
Elliptic PDE
Lowest
Finite Element Method
Poisson Model
Finite element method
Error analysis
A Posteriori Error Analysis
Inf-sup Condition
Weak Formulation
Test function
Discretization
Numerical Experiment
Experiments

Cite this

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
Carstensen, C. ; Gallistl, D. ; Hellwig, F. ; Weggler, L. / Low-order dPG-FEM for an elliptic PDE. In: Computers and mathematics with applications. 2014 ; Vol. 68, No. 11. pp. 1503-1512.
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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, vol. 68, no. 11, pp. 1503-1512. https://doi.org/10.1016/j.camwa.2014.09.013

Low-order dPG-FEM for an elliptic PDE. / Carstensen, C.; Gallistl, D.; Hellwig, F.; Weggler, L.

In: Computers and mathematics with applications, Vol. 68, No. 11, 2014, p. 1503-1512.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Hellwig, F.

AU - Weggler, L.

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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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JO - Computers and mathematics with applications

JF - Computers and mathematics with applications

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