Error estimates of \(H^1\)-Galerkin mixed methods for the viscoelasticity wave equation. (English) Zbl 1240.74023
Summary: \(H^1\)-Galerkin mixed methods are proposed for the viscoelasticity wave equation. Depending on the physical quantities of interest, two methods are discussed. The optimal error estimates and the proof of existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension. The methods do not require the Ladyshenskaya-Babuška-Brezzi condition.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
