To solve parabolic problems a hybrid finite element method (HFEM) is introduced to numerically solve the bi-dimensional heat problem combined with finite difference time integration schemes. Such a formulation has been designed considering discontinuous spatial discretizations with continuity along the interface imposed via a Lagrange multiplier. The accuracy and efficiency of the proposed hybrid method are compared against the standard Galerkin method. Furthermore, the HFEM is applied to treat the spurious spatial oscillation problems commonly present in the continuous Galerkin semi-discrete approaches when applied to parabolic problems. For an appropriate choice of the stabilization parameter, numerical simulations will show that the HFEM is well suited to remediate these pathologies.
finite differences; hybrid methods; heat equation; stabilization
