- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Volume:69 Issue:1
- A space-time discontinuous Galerkin method for linear hyperbolic PDE`s with high frequencies
A space-time discontinuous Galerkin method for linear hyperbolic PDE`s with high frequencies
Authors : Şuayip TOPRAKSEVEN
Pages : 213-231
Doi:10.31801/cfsuasmas.544522
View : 100 | Download : 10
Publication Date : 2020-06-30
Article Type : Research Paper
Abstract :The main purpose of this paper is to describe a space-time discontinuous Galerin insert ignore into journalissuearticles values(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.Keywords : Discontinuous Galerkin finite element methods, space time discontinuous Galerkin methods, hyperbolic problems, high frequency solutions
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