On an a posteriori error analysis of mixed finite element Galerkin approximations to a second order wave equation
Provides rigorous error control for mixed finite element methods applied to wave propagation problems, which is important for adaptive mesh refinement in computational wave simulation.
The paper develops a posteriori error estimates for mixed finite element approximations to second-order wave equations, achieving L∞(L2)-norm bounds under minimal regularity for both semidiscrete and fully discrete schemes.
In this article, a posteriori error analysis is developed for mixed finite element Galerkin approximations to a second order linear hyperbolic equation. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker's technique introduced earlier by G. Baker ( SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equation, a posteriori error estimates of the displacement in L{\infty}(L2)-norm for the semidiscrete scheme are derived under minimal regularity. Finally, a first order implicit-in-time discrete scheme is analyzed and a posteriori error estimators are established.