Mixed virtual element method for the Helmholtz transmission eigenvalue problem on polytopal meshes
Jian Meng, Gang Wang, Liquan Mei
Abstract
Abstract In this paper we propose and analyze a mixed virtual element method for the Helmholtz transmission eigenvalue problem, which is a fourth order, nonlinear and non-self-adjoint eigenvalue problem and is important in the inverse scattering theory. The conforming virtual element is used for discretization. We prove correct spectral approximation and error estimates of the discrete scheme. Finally, we show several numerical examples to verify the theoretical results and present the performance of different stabilization parameters and the comparison with the $C^{1}$ virtual element method.
Topics & Concepts
MathematicsDiscretizationHelmholtz equationEigenvalues and eigenvectorsPolygon meshElement (criminal law)Helmholtz free energyFinite element methodTransmission (telecommunications)Mathematical analysisInverseNonlinear systemApplied mathematicsGeometryComputer scienceBoundary value problemPolitical scienceQuantum mechanicsLawTelecommunicationsPhysicsThermodynamicsAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical MethodsElectromagnetic Scattering and Analysis