Adaptive FE Eigenvalue Computation with Applications to Hydrodynamic Stability

摘要: We present an adaptive finite element method for the solution of eigenvalue problems associated with linearized stability analysis non-linear operators in context hydrodynamic theory. The goal is to obtain a posteriori information about location critical eigenvalues, their possible degeneration and corresponding pseudo-spectrum. general framework Dual Weighted Residual (DWR) local mesh adaptation which driven by residual- sensitivity-based information. basic idea embed approximation into Galerkin methods nonlinear variational equations DWR already well developed. evaluation these error representations results bounds approximate eigenvalues reflecting errors discretization problem as those linearization only approximately known base solution. From estimates indicators are derived economical meshes can be constructed.