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arXiv · 2407.03777

Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem

Neela Nataraj·Ricardo Ruiz-Baier·Aamir Yousuf
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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 $H^2_0(\Omega)$ 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$^0$ interior} penalty schemes for space discretization, that validate the theoretical error estimates.

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Neela Nataraj, Ricardo Ruiz-Baier, Aamir Yousuf. 2024-07-04. Semi and fully-discrete analysis of lowest-order nonstandard finite element methods for the biharmonic wave problem. https://arxiv.org/abs/2407.03777

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