The size function for a HDG method applied to the Helmholtz problem

In this work, we propose a hybridized Continuous/Discontinuous Galerkin formulation for the Helmholtz problem that works with a continuous trace space. Additionally, it is done a static condensation analysis where we obtain a global system that is smaller than global systems generated by other current hybrid methods. Therefore, we conjecture that the computational effort of our formulation is lower than that of the classic DG methods. Furthermore, static condensation is proved as being a well-posed problem from a certain degree of mesh refinement. As result, we present the computational time for the method with continuous trace space compared with the computational time of a continuous Galerkin approach for a fixed polynomial approximation and different mesh refinements. Numerical results show the robustness and accuracy of our formulation as well as the potentiality of the present method.