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 $L^2$ 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.

不连续的Petrov-Galerkin（DPG）方法可最大程度地减少非标准规范中的残差。本文表明，该残差的最小化等效于一个残差的最小化。${\mathrm{大号}}^2$规范。由于这种残差是从最小二乘有限元方法中众所周知的，因此这种新颖的解释允许将最小二乘法的结果扩展到DPG方法，反之亦然。本文通过验证Helmholtz方程的DPG方法的渐近精确性结果，线性弹性的无锁DPG方法的设计以及对光谱条件数的研究，证明了这种可能性的好处。