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