A superconvergent alpha finite element method (SαFEM) for acoustic problems

With the aim to overcome the “overly-soft” property of FEM and decrease the numerical error, a superconvergent alpha FEM (SαFEM) using the standard triangle meshes is proposed to solve acoustic problems. Based on this method, a linear acoustic pressure gradient is obtained from the original constant acoustic pressure gradient using a particular numerical operation. Using a appropriate parameter α, which is equipped in the procedure, SαFEM could obtain appropriate stiffness. Therefore, the numerical error in acoustic analysis based on FEM can be significantly decreased. Through a number of numerical examples, we can find that this proposed SαFEM has superconvergence property and are able to acquire better solutions compared to FEM in acoustic analysis.