A space-time discontinuous Galerkin method for linear hyperbolic PDE's with high frequencies

Şuayip Toprakseven
2020 Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics  
The main purpose of this paper is to describe a space-time discontinuous Galerkin (DG) method based on an extended space-time approximation space for the linear ...rst order hyperbolic equation that contains a high frequency component. We extend the space-time DG spaces of tensorproduct 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
more » ... time DG method with the extended ...nite element method. The basic principle of the method is integrating the features of the partial di¤erential equation with the standard space-time spaces in the approximation. We present error analysis of the proposed spacetime DG method for the linear ...rst 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 ...ndings and demonstrate the e¤ects of the proposed method. Mathematics Subject Classi...cation. Primary 65M60,65M12,65M15; Secondary 35L03, 35L65. Key words and phrases. Discontinuous Galerkin ...nite element methods, space-time discontinuous Galerkin methods, hyperbolic problems, high frequency solutions. c 2 0 2 0 A n ka ra U n ive rsity C o m m u n ic a tio n s Fa c u lty o f S c ie n c e s U n ive rsity o f A n ka ra -S e rie s A 1 M a th e m a tic s a n d S ta tistic s 213 214ŞUAYIP TOPRAKSEVEN
doi:10.31801/cfsuasmas.544522 fatcat:dxf6aapzivex5kxv4teynafa2q