An analysis of the practical DPG method

An analysis of the practical DPG method

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, which when applied to the trial spa...

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Bibliographic Details
Published in:Mathematics of computation Vol. 83; no. 286; pp. 537 - 552
Main Authors: GOPALAKRISHNAN, J., QIU, W.
Format: Journal Article
Language:English
Published: American Mathematical Society 01-03-2014
Subjects:
Discontinuous Galerkin
Petrov-Galerkin
DPG method
ultraweak formulation
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Summary: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, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T. In practical computations, T on each mesh element. We show that this approximation maintains optimal convergence rates, provided that r\ge p+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.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-2013-02721-4