A nonconforming Trefftz virtual element method for the Helmholtz problem

A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element

A symmetric Trefftz-DG formulation based on a local boundary element method for the solution of the Helmholtz equation

A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly...

Applications of the direct Trefftz boundary element method to the free-vibration problem of a membrane.

In this paper, the direct Trefftz method is applied to solve the free-vibration problem of a membrane. In the direct Trefftz method, there exists no spurious eigenvalue. However, an ill-posed nature of numerical instability encountered in the direct Trefftz method requires some treatments. The Tikhonov's regularization method and generalized singular-value decomposition method are used to deal ...

A survey of Trefftz methods for the Helmholtz equation

Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain oscillating basis functions and may achieve better approximation properties than classical piecewise-polynomial spaces. We review the construction and properties ...

A Hybridized Crouziex-Raviart Nonconforming Finite Element and Discontinuous Galerkin Method for a Two-Phase Flow in the Porous Media

In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The p...