Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics



+44 (0)20 7594 3468colin.cotter




755Huxley BuildingSouth Kensington Campus






BibTex format

author = {McRae, ATT and Cotter, CJ and Budd, CJ},
doi = {10.1137/16M1109515},
journal = {SIAM Journal on Scientific Computing},
pages = {A1121--A1148},
title = {Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements},
url = {},
volume = {40},
year = {2018}

RIS format (EndNote, RefMan)

AB - In moving mesh methods, the underlying mesh is dynamically adapted withoutchanging the connectivity of the mesh. We specifically consider the generationof meshes which are adapted to a scalar monitor function throughequidistribution. Together with an optimal transport condition, this leads to aMonge-Amp\`ere equation for a scalar mesh potential. We adapt an existingfinite element scheme for the standard Monge-Amp\`ere equation to this meshgeneration problem; this is a mixed finite element scheme, in which an extradiscrete variable is introduced to represent the Hessian matrix of secondderivatives. The problem we consider has additional nonlinearities over thebasic Monge-Amp\`ere equation due to the implicit dependence of the monitorfunction on the resulting mesh. We also derive the equivalentMonge-Amp\`ere-like equation for generating meshes on the sphere. The finiteelement scheme is extended to the sphere, and we provide numerical examples.All numerical experiments are performed using the open-source finite elementframework Firedrake.
AU - McRae,ATT
AU - Cotter,CJ
AU - Budd,CJ
DO - 10.1137/16M1109515
EP - 1148
PY - 2018///
SP - 1121
TI - Optimal-transport-based mesh adaptivity on the plane and sphere using finite elements
T2 - SIAM Journal on Scientific Computing
UR -
UR -
UR -
VL - 40
ER -