A Hybrid–Stabilized FEM Method Applied to Heat Conduction Equation

Resumo

In this work, it is performed a numerical analysis of a totaly discrete formulation for the transient heat
conduction problem. This formulation is constructed by using a discontinuous hybrid stabilized finite element
method in space combined with a high order finite difference approximation (Crank-Nicolson method) for the
temporal dependency. The computational methodology used to solve the formulation is a static condensation
scheme resulting in a global system related only with the Lagrange multiplier associated with the trace of the
temperature at the edges of the elements and local problems that are solved for the temperature. In doing so, the
number of the degrees of freedom of the global system is reduced. Numerical results are presented confirming the
optimal rates of convergence obtained in the numerical analysis.