Section: New Results
New mixed hybrid elements combining Lagrange polynomials and plane waves for the solution of the Helmholtz equation
We propose a new mixed-hybrid-type solution methodology to be applied for solving high-frequency Helmholtz problems. The proposed approach distinguishes itself from similar methods by a local approximation of the solution with oscillated finite elements polynomials satisfying the wave equation. The weak continuity of the solution across the element interfaces is enforced using Lagrange multipliers. A convergence analysis of the method has been performed an it shows the strong stability properties of this new discretization. Numerical results obtained in the case of two-dimensional waveguide problems illustrate the computational efficiency of the proposed solution methodology. Now, we are applying the new finite element method for solving the seismic wave equation.