French, DonaldVaughan, BenjaminToprakseven, Şuayip2022-03-072022-03-072021French D., Vaughan, B., & Toprakseven, Ş. (2021). Error analysis of an extended discontinuous galerkin method for highly-oscillatory problems, Yıldız Teknik Üniversitesi, 39 (5), 64-73.https://hdl.handle.net/11494/3738In this report we introduce an extended discontinuous Galerkin (XDG) method. Our XDG scheme is based on the Babuska-Zlamal approach and we apply it to a class of prototype elliptic boundary value problems that have solutions consisting of smooth functions perturbed by a set of high frequency modes which occupy a narrow band. The XDG scheme we study is enriched by trigonometric functions that cover the range of these perturbations. A theoretical error analysis is provided that shows the method converges and gives specifics on its accuracy. Computations with the XDG scheme further demonstrate the efficacy of this approach.eninfo:eu-repo/semantics/openAccessDiscontinuous GalerkinExtended discontinuous GalerkinHigh frequenciesElliptic boundary value problemArticle395647310.14744/sigma.2021.00043N/A