Using Plane Waves as Base Functions for Solving Time Harmonic Equations with the Ultra Weak Variational Formulation

By O. Cessenat, B. Després. 2003

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A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation (2013, methodology): “To the end of alleviating the pollution eﬀect, various continuous or discontinuous ﬁnite element methods have been developed in the literature for solving the Helmholtz equation with large wave numbers [4, 5, 26, 27, 8, 9, 16, 17, 18, 3, 12, 14, 15, 20].”
A review of finite-element methods for time-harmonic acoustics (2006, methodology): “The ultra-weak variational formulation [37, 38, 101] is another approach to using discontinuous local plane-wave solutions of the Helmholtz equation on each element.”
A survey of finite element methods for time-harmonic acoustics (2006, background): “Various implementations of such hybrid approaches have been suggested [87,88].”
A new weak Galerkin finite element method for the Helmholtz equation (2015, methodology): “Many numerical schemes have been developed and analyzed for the Helmholtz equation using finite element methods or other numerical methods [1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29] and the references therein.”
PLANE WAVE DISCONTINUOUS GALERKIN METHODS: ANALYSIS OF THE h-VERSION ∗, ∗∗ (2009, methodology): “The ultra-weak variational formulation (UWVF) of Cessenat and Després, see [10,11], is obtained by choosing the numerical fluxes in (2.”