Elliptic heat conduction specialized applications involving high gradients: Local discontinuous Galerkin finite element method - Part 1

In this paper, a Local Discontinuous Galerkin (LDG) finite element method is described for solving specialized heat conduction problems involving sharp/high gradients. The advantages of LDG method over the traditional continuous Galerkin (CG) finite element method are presented. It is further shown in the problems involving sharp and/or high gradients, that the LDG method is less expensive, requiring a fewer number of degrees of freedom as compared to the continuous Galerkin method to capture the peak value of the gradients. Simple one- and two-dimensional applications are illustrated to describe the applicability to this class of field problems.