TY - JOUR
T1 - A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation
AU - Thompson, Travis
N1 - KAUST Repository Item: Exported on 2021-04-02
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work was supported by AFOSR grant FA99550-12-0358, National Science Foundation grants DMS-1217262 and DMS-1015984 and was partially supported by award KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST) (Texas A&M University, P.I. J.-L. Guermond) in addition to the partial support of National Science Foundation grant DMS-1312391 (Rice University, P.I. B. Rivière).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2016/9
Y1 - 2016/9
N2 - A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.
AB - A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.
UR - http://hdl.handle.net/10754/668483
UR - https://linkinghub.elsevier.com/retrieve/pii/S037704271630098X
UR - http://www.scopus.com/inward/record.url?scp=84962331737&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2016.02.042
DO - 10.1016/j.cam.2016.02.042
M3 - Article
SN - 0377-0427
VL - 303
SP - 229
EP - 248
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -