Numerical solution of a singularly perturbed problem by using hybridizable discontinuous Galerkin method


Karaaslan M. F.

International Conference on Analysis and its Applications (ICAA 2016), Kırşehir, Türkiye, 12 - 15 Temmuz 2016, ss.183

  • Basıldığı Şehir: Kırşehir
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayısı: ss.183

Özet

In this work, a current numerical method called as hybridizable discontinuous Galerkin (HDG) method is presented for solving a type of singularly perturbed problem (SPP) with boundary conditions (BCs). The main feature of the HDG method is that it can be implemented in an efficient way through a hybridization procedure which reduces the globally coupled unknowns to approximations at the element boundaries. For stability of the global linear system which is constructed for SPP, it is a crucial point to choose stability parameter.It has to be suitably defined to guarantee the existence and uniqueness of the numerical solution. However, the associated matrix in the system is tridiagonal, symmetric ve positive definite. Thus, HDG method is accomplishedly implemented ordinary or partial differential equations. From this point of view, HDG approximation of the SPP with boundary layer is examinedon some examples for𝐿 2 -norm.