Numerical solution of the acoustic wave equation using Raviart-Thomas elements
Journal of Computational and Applied Mathematics
Performance of numerically computed quadrature points
Applied Numerical Mathematics
Weighted quadrature rules for finite element methods
Journal of Computational and Applied Mathematics
Optimal Error Estimates for the Fully Discrete Interior Penalty DG Method for the Wave Equation
Journal of Scientific Computing
Numerical simulation of a guitar
Computers and Structures
Arbitrary High-Order Finite Element Schemes and High-Order Mass Lumping
International Journal of Applied Mathematics and Computer Science - Scientific Computation for Fluid Mechanics and Hyperbolic Systems
Journal of Computational and Applied Mathematics
Explicit Runge-Kutta residual distribution schemes for time dependent problems: Second order case
Journal of Computational Physics
Explicit local time-stepping methods for Maxwell's equations
Journal of Computational and Applied Mathematics
High-order implicit hybridizable discontinuous Galerkin methods for acoustics and elastodynamics
Journal of Computational Physics
High-order explicit local time-stepping methods for damped wave equations
Journal of Computational and Applied Mathematics
Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves
Journal of Computational Physics
Mimetic finite difference method
Journal of Computational Physics
Hi-index | 0.03 |
In this article, we construct new higher order finite element spaces for the approximation of the two-dimensional (2D) wave equation. These elements lead to explicit methods after time discretization through the use of appropriate quadrature formulas which permit mass lumping. These formulas are constructed explicitly. Error estimates are provided for the corresponding semidiscrete problem. Finally, higher order finite difference time discretizations are proposed and various numerical results are shown.