Combining Stabilized Finite Element Methods

We combine the Galerkin-least-squares (GLS) and the Galerkin-gradient-least-squares (GGLS) methods to simulate scalar linear second order partial differential equations which include second, first and zero order terms. Assuming a strictly positive coefficient for the second order term, the resulting method is proven convergent for a wide range of the coefficients multiplying each term. The stability parameters are designed to take into account the presence of both modifications to the Galerkin method. Numerical results atest the good stability characteristics of the method.