A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D

摘要: The phase error, or the pollution effect in finite element solution of wave propagation problems, is a well known phenomenon that must be confronted when solving problems high-frequency range. This paper presents new method with no errors for one-dimensional (1D) time-harmonic using ideas hold promise multidimensional case. constructed within framework discontinuous Petrov-Galerkin (DPG) optimal test functions. We have previously shown such methods select solutions are best possible approximations an energy norm dual to any selected space norm. In this paper, we advance by asking what achieves error reduction given answered specific case Helmholtz equation L^2-norm as obtain uniform stability respect number. illustrate number 1D numerical experiments, piecewise polynomial hp spaces trial and its corresponding functions computed approximately locally. A theoretical analysis also developed.