# Robust operator estimates and the application to substructuring methods for first-order systems

Christian Wieners; Barbara Wohlmuth

- Volume: 48, Issue: 5, page 1473-1494
- ISSN: 0764-583X

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topWieners, Christian, and Wohlmuth, Barbara. "Robust operator estimates and the application to substructuring methods for first-order systems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.5 (2014): 1473-1494. <http://eudml.org/doc/273259>.

@article{Wieners2014,

abstract = {We discuss a family of discontinuous Petrov–Galerkin (DPG) schemes for quite general partial differential operators. The starting point of our analysis is the DPG method introduced by [Demkowicz et al., SIAM J. Numer. Anal. 49 (2011) 1788–1809; Zitelli et al., J. Comput. Phys. 230 (2011) 2406–2432]. This discretization results in a sparse positive definite linear algebraic system which can be obtained from a saddle point problem by an element-wise Schur complement reduction applied to the test space. Here, we show that the abstract framework of saddle point problems and domain decomposition techniques provide stability and a priori estimates. To obtain efficient numerical algorithms, we use a second Schur complement reduction applied to the trial space. This restricts the degrees of freedom to the skeleton. We construct a preconditioner for the skeleton problem, and the efficiency of the discretization and the solution method is demonstrated by numerical examples.},

author = {Wieners, Christian, Wohlmuth, Barbara},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {first-order systems; Petrov–Galerkin methods; saddle point problems; substructuring methods; discontinuous Petrov-Galerkin method; preconditioning},

language = {eng},

number = {5},

pages = {1473-1494},

publisher = {EDP-Sciences},

title = {Robust operator estimates and the application to substructuring methods for first-order systems},

url = {http://eudml.org/doc/273259},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Wieners, Christian

AU - Wohlmuth, Barbara

TI - Robust operator estimates and the application to substructuring methods for first-order systems

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 5

SP - 1473

EP - 1494

AB - We discuss a family of discontinuous Petrov–Galerkin (DPG) schemes for quite general partial differential operators. The starting point of our analysis is the DPG method introduced by [Demkowicz et al., SIAM J. Numer. Anal. 49 (2011) 1788–1809; Zitelli et al., J. Comput. Phys. 230 (2011) 2406–2432]. This discretization results in a sparse positive definite linear algebraic system which can be obtained from a saddle point problem by an element-wise Schur complement reduction applied to the test space. Here, we show that the abstract framework of saddle point problems and domain decomposition techniques provide stability and a priori estimates. To obtain efficient numerical algorithms, we use a second Schur complement reduction applied to the trial space. This restricts the degrees of freedom to the skeleton. We construct a preconditioner for the skeleton problem, and the efficiency of the discretization and the solution method is demonstrated by numerical examples.

LA - eng

KW - first-order systems; Petrov–Galerkin methods; saddle point problems; substructuring methods; discontinuous Petrov-Galerkin method; preconditioning

UR - http://eudml.org/doc/273259

ER -

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