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Abstract
Abstract This paper discusses lowest-order nonstandard finite element methods for space discretization and explicit and implicit schemes for time discretization of the biharmonic wave equation with clamped boundary conditions. A modified Ritz projection operator defined on H 0 2 ( Ω ) {H^{2}_{0}(\Omega)} ensures error estimates under appropriate regularity assumptions on the solution. Stability results and error estimates of optimal order are established in suitable norms for the semidiscrete and explicit/implicit fully-discrete versions of the proposed schemes. Finally, we report on numerical experiments using explicit and implicit schemes for time discretization and Morley, discontinuous Galerkin, and C 0 {C^{0}} interior penalty schemes for space discretization, that validate the theoretical error estimates.
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