Galerkin gradient least-squares formulations for transient conduction heat transfer Original Research Article

This paper presents the benefits provided by the use of the Galerkin gradient least-squares (GGLS) method for transient conduction heat transfer. The consistency of the GLS method for this type of problem is also discussed. The GGLS method is compared with standard Galerkin formulation on problems having an analytical solution: a semi-infinite solid solved on one- and three-dimensional meshes and a three-dimensional thin plate. For three-dimensional applications, the principle of including gradient least-squares terms is extended to stabilize Robin (convection) boundary conditions. Numerical simulations show that additional boundary gradient least-squares terms improve the behavior of the solution on boundaries subject to convection boundary conditions. New procedures used to obtain the GLS and GGLS stabilized finite element formulations are also presented. The methodology consists in modifying the equation to be solved and then to obtain the variational equation by a standard Galerkin method.