Discontinuous Galerkin methods with Trefftz approximations
نویسندگان
چکیده
منابع مشابه
Multiplicative Schwarz Methods for Discontinuous Galerkin Approximations of Elliptic Problems
In this paper we introduce and analyze some non-overlapping multiplicative Schwarz methods for discontinuous Galerkin (DG) approximations of elliptic problems. The construction of the Schwarz preconditioners is presented in a unified framework for a wide class of DG methods. For symmetric DG approximations we provide optimal convergence bounds for the corresponding error propagation operator, a...
متن کاملTransparent boundary conditions for a discontinuous Galerkin Trefftz method
The modeling and simulation of electromagnetic wave propagation is often accompanied by a restriction to bounded domains which requires the introduction of artificial boundaries. The corresponding boundary conditions should be chosen in order to minimize parasitic reflections. In this paper, we investigate a new type of transparent boundary condition for a discontinuous Galerkin Trefftz finite ...
متن کاملDiscontinuous Galerkin methods
This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience.We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block-diagonal. This renders the methods highly parallelizable when applied to hyperbolic problems. Another co...
متن کاملError analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations
In this paper, we extend to the time-harmonic Maxwell equations the p–version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a me...
متن کاملMixed Discontinuous Galerkin Methods with Minimal Stabilization
We will address the problem of finding the minimal necessary stabilization for a class of Discontinuous Galerkin (DG) methods in mixed form. In particular, we will present a new stabilized formulation of the Bassi–Rebay method (see Ref. 1 for the original unstable method) and a new formulation of the Local Discontinuous Galerkin method (LDG), introduced in 1998 by Cockburn and Shu.2 It will be ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2014
ISSN: 0377-0427
DOI: 10.1016/j.cam.2014.01.033