Abstract
We consider a family of fully discrete finite element schemes for solving a viscous wave equation, where the time integration is based on the Newmark method. A rigorous stability analysis based on the energy method is developed. Optimal error estimates in both time and space are obtained. For sufficiently smooth solutions, it is demonstrated that the maximal error in the L 2-norm over a finite time interval converges optimally as O(h p+1+Δts), where p denotes the polynomial degree, s=1 or 2, h the mesh size, and Δt the time step.
Original language | English |
---|---|
Pages (from-to) | 750-767 |
Number of pages | 18 |
Journal | Numerical Functional Analysis and Optimization |
Volume | 32 |
Issue number | 7 |
DOIs | |
Publication status | Published - Jul 2011 |
Keywords
- Energy method
- Error estimates
- Finite element method
- Viscous wave equation
ASJC Scopus subject areas
- Analysis
- Signal Processing
- Computer Science Applications
- Control and Optimization