Temporal stability of collocation, Petrov–Galerkin, and other non-symmetric methods in elastodynamics and an energy conserving time integration

Non-symmetric matrices may arise in the discretization of self-adjoint problems when a Petrov–Galerkin, collocation, or finite-volume method is employed. While these methods have been widely applied, this paper it shown that use non-symmetric incompatable with conservation energy elastodynamics. First, consistency between continuous forms momentum equation and examined. It linear equivalent to provided solution sufficiently smooth. The semi-discrete counterparts are then analyzed, where demonstrated they also equivalent, but only conditionally: mass stiffness must be symmetric. As result, employing elastodynamics artificially generate dissipate energy. fully discrete Newmark time integration examined unconditionally unstable algorithms arise. An energy-conserving algorithm proposed which provides stability solutions systems. collocation employed numerical examples demonstrate issues effectiveness methodology. • Analysis energy–momentum on level Temporal analysis solving by type Unconditionally for Petrov–Galerkin A exactly conserve