Boundary observability for the space-discretizations of the 1 — d wave equation
Copyright policy )Boundary observability for the space-discretizations of the 1 — d wave equation
Summary: We consider the finite-difference and finite-element space discretization of the \(1-d\) wave equation with homogeneous Dirichlet boundary conditions in a bounded interval. We analyze the problem of estimating the total energy of solutions in terms of the energy concentrated on the boundary, uniformly as the net-spacing \(h\to 0\). We prove that there is no such a uniform bound due to spurious high frequencies. We prove however an uniform bound in suitable subspaces of solutions that eventually cover the whole energy space.
Controllability, boundary control, Numerical optimization and variational techniques, Observability, Control/observation systems governed by partial differential equations, total energy of solutions, finite-element, finite-difference, boundary observability, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Wave equation, wave equation, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
Controllability, boundary control, Numerical optimization and variational techniques, Observability, Control/observation systems governed by partial differential equations, total energy of solutions, finite-element, finite-difference, boundary observability, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Wave equation, wave equation, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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