Dispersion and Eigenvector Error Analysis of Simplicial Cubic Hermite Elements for 1-D and 2-D Wave Propagation Problems

Dispersion error analysis can help to assess the performance of finite-element discretizations of the wave equation. Although less general than the convergence estimates offered by standard finite-element error analysis, it can provide more detailed insight as well as practical guidelines in terms of the number of elements per wavelength needed...

Numerical noise suppression for wave propagation with finite elements in first-order form by an extended source term

Finite elements can, in some cases, outperform finite-difference methods for modelling wave propagation in complex geological models with topography. In the weak form of the finiteelement method, the delta function is a natural way to represent a point source. If, instead of the usual second-order form, the first-order form of the wave equation...

An improved source term for finite-element modelling with the stress-velocity formulation of the wave equation

For seismic modelling, imaging and inversion, finite-difference methods are still the workhorse of the industry despite their inability to meet the increasing demand for improved accuracy in subsurface imaging. Finiteelement methods offer better accuracy but at a higher computational cost. A stress-velocity formulation with linear elements and...

Should We Use the First- or Second-order Formulation with Spectral Elements for Seismic Modelling?

The second-order formulation of the wave equation is often used for spectral-element discretizations. For some applications, however, a first-order formulation may be desirable. It can, in theory, provide much better accuracy in terms of numerical dispersion if the consistent mass matrix is used and the degree of the polynomial basis functions...

Dispersion analysis of finite-element schemes for a first-order formulation of the wave equation

We investigated one-dimensional numerical dispersion curves and error behaviour of four finite-element schemes with polynomial basis functions: the standard elements with equidistant nodes, the Legendre-Gauss-Lobatto points, the Chebyshev-Gauss-Lobatto nodes without a weighting function and with. Mass lumping, required for efficiency reasons and...