Research Note

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

Mulder, W.A. (TU Delft Applied Geophysics and Petrophysics; Shell Global Solutions International B.V.)

2020

The representation of a force or moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on one-dimensional elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in three dimensions on continuous mass-lumped tetrahedral elements show a similar error behaviour as in the one-dimensional case, although in three dimensions the loss of accuracy for the moment source is not a severe as a full order.

Computing aspects
Elastics
Mathematical formulation
Modelling
Seismics

http://resolver.tudelft.nl/uuid:bb5438bb-cc07-499f-9a09-96d64fd29996

https://doi.org/10.1111/1365-2478.13013

2021-07-18

0016-8025

Geophysical Prospecting, 68 (8), 2598-2603

Accepted Author Manuscript

Institutional Repository

journal article

© 2020 W.A. Mulder