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

Christian Wieners, Barbara Wohlmuth (2014)

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

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....

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