A space-time discontinuous Galerkin method for linear hyperbolic PDE's with high frequencies
No Thumbnail Available
Files
Date
2020-06-30
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi Fen Fakültesi
Abstract
The main purpose of this paper is to describe a space-time discontinuous Galerin (DG) method based on an extended space-time approximation space for the linear first order hyperbolic equation that contains a high frequency component. We extend the space-time DG spaces of tensor-product of polynomials by adding trigonometric functions in space and time that capture the oscillatory behavior of the solution. We construct the method by combining the basic framework of the space-time DG method with the extended finite element method. The basic principle of the method is integrating the features of the partial differential equation with the standard space-time spaces in the approximation. We present error analysis of the space-time DG method for the linear first order hyperbolic problems. We show that the new space-time DG approximation has an improvement in the convergence compared to the space-time DG schemes with tensor-product polynomials. Numerical examples verify the theoretical findings and demonstrate the effects of the proposed method.
Description
Keywords
Discontinuous Galerkin finite element methods, Space-time discontinuous Galerkin methods, Hyperbolic problems