Imperial College London


Faculty of EngineeringDepartment of Aeronautics

Professor of Computational Fluid Mechanics



+44 (0)20 7594 5052s.sherwin Website




313BCity and Guilds BuildingSouth Kensington Campus






BibTex format

author = {Xu, H and Cantwell, C and Monteserin, C and Eskilsson, C and Engsig-Karup, AP and Sherwin, SJ},
doi = {10.1007/s42241-018-0001-1},
journal = {Journal of Hydrodynamics},
pages = {1--22},
title = {Spectral/hp element methods: Recent developments, applications, and perspectives},
url = {},
volume = {30},
year = {2018}

RIS format (EndNote, RefMan)

AB - The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element method in more complex science and engineering applications are discussed.
AU - Xu,H
AU - Cantwell,C
AU - Monteserin,C
AU - Eskilsson,C
AU - Engsig-Karup,AP
AU - Sherwin,SJ
DO - 10.1007/s42241-018-0001-1
EP - 22
PY - 2018///
SN - 1001-6058
SP - 1
TI - Spectral/hp element methods: Recent developments, applications, and perspectives
T2 - Journal of Hydrodynamics
UR -
UR -
VL - 30
ER -