Abstract
The discontinuous Petrov–Galerkin (DPG) method minimizes a residual in a non-standard norm. This paper shows that the minimization of this residual is equivalent to the minimization of a residual in a L2 norm. Since such residuals are well known from least squares finite element methods, this novel interpretation allows to extend results for least squares methods to the DPG method and vice versa. This paper exemplifies the benefits of this possibility by the verification of an asymptotic exactness result for a DPG method for the Helmholtz equation, the design of a locking-free DPG method for linear elasticity, and an investigation of the spectral condition number.
Published Version
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