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• W2952674705 abstract "In this work we give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree $p$ on each mesh element. Earlier works showed that there is a trial-to-test operator $T$, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator $T$ is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply $T$. In practical computations, $T$ is approximated using polynomials of some degree $r > p$ on each mesh element. We show that this approximation maintains optimal convergence rates, provided that $rge p+N$, where $N$ is the space dimension (two or more), for the Laplace equation. We also prove a similar result for the DPG method for linear elasticity. Remarks on the conditioning of the stiffness matrix in DPG methods are also included." @default.
• W2952674705 created "2019-06-27" @default.
• W2952674705 creator A5022236310 @default.
• W2952674705 creator A5059376708 @default.
• W2952674705 date "2011-07-21" @default.
• W2952674705 modified "2023-09-24" @default.
• W2952674705 title "An analysis of the practical DPG method" @default.
• W2952674705 cites W1963659668 @default.
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• W2952674705 doi "https://doi.org/10.48550/arxiv.1107.4293" @default.
• W2952674705 hasPublicationYear "2011" @default.
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