A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation (Communications in Computational Physics, 2014)
A weak Galerkin (WG) method is introduced and numerically tested for theHelmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the mass conservation property. At the same time, the WG finiteelement formulation is symmetric and parameter free. Several test scenarios are designed for a numerical investigation on the accuracy, convergence, and robustness ofthe WG method in both inhomogeneous and homogeneous media over convex andnon-convex domains. Challenging problems with high wave numbers are also examined. Our numerical experiments indicate that the weak Galerkin is a finite elementtechnique that is easy to implement, and provides very accurate and robust numericalsolutions for the Helmholtz problem with high wave numbers.