Continuous Interior Penalty Finite Element Method With PML For Helmholtz Equation With High Wave Number

Wave is ubiquitous. It is significant to geoscience, petroleum engineering, telecom-munication, and defense industry. Mathematically, wave propagation problems are described by hyperbolic partial differential equations. The simplest prototype wave scattering problem is the Helmholtz equation considered in this thesis. To compute the solution of the above problem, due to finite memory and speed limitations of com-puters, one needs first to formulate the problem as a finite domain problem. Jean-Pierre Berenger put forward the perfectly matched layer (PML) technique in1994for the task. It has been proved theoretically that the PML medium can absorb all of the outgoing waves neglecting direction and frequency without any reflection, and the waves decay exponentially in magnitude into the PML medium. In this thesis we adopt this popular technique to truncate the unbounded domain. On the other hand, large wave number can cause the pollution error. In this thesis we use the continuous interior penalty finite element methods (CIP-FEM) to reduce the pollution error.In this thesis, we combine the PML technique with the CIP-FEM to design the numerical scheme for solving the Helmholtz equation. And according to existing lit-eratures, we make some guesswork for stability and error estimates. By doing lots of numerical tests, we have kept improving the numerical scheme, and have verified our guesswork successfully.