DeepAI
Log In Sign Up

C^1-conforming variational discretization of the biharmonic wave equation

07/08/2021
by   Markus Bause, et al.
0

Biharmonic wave equations are of importance to various applications including thin plate analyses. In this work, the numerical approximation of their solutions by a C^1-conforming in space and time finite element approach is proposed and analyzed. Therein, the smoothness properties of solutions to the continuous evolution problem is embodied. High potential of the presented approach for more sophisticated multi-physics and multi-scale systems is expected. Time discretization is based on a combined Galerkin and collocation technique. For space discretization the Bogner–Fox–Schmit element is applied. Optimal order error estimates are proven. The convergence and performance properties are illustrated with numerical experiments.

READ FULL TEXT
01/28/2022

Convergence of a continuous Galerkin method for mixed hyperbolic-parabolic systems

We study the numerical approximation by space-time finite element method...
08/22/2019

Galerkin-collocation approximation in time for the wave equation and its post-processing

We introduce and analyze a class of Galerkin-collocation discretization ...
01/02/2021

The Estimation of Approximation Error using the Inverse Problem and the Set of Numerical Solutions

The Inverse Problem for the estimation of a point-wise approximation err...
12/12/2019

A numerical study of the pollution error and DPG adaptivity for long waveguide simulations

High-frequency wave propagation has many important applications in acous...
08/17/2020

Superconvergence of time invariants for the Gross-Pitaevskii equation

This paper considers the numerical treatment of the time-dependent Gross...
06/28/2021

A direction preserving discretization for computing phase-space densities

Ray flow methods are an efficient tool to estimate vibro-acoustic or ele...