Goal-Oriented Error Estimation and Mesh Adaptation for Shallow Water Modelling

This is a Preprint and has not been peer reviewed. The published version of this Preprint is available: https://doi.org/10.1007/s42452-020-2745-9.


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Joseph Wallwork , Nicolas Barral, Stephan C. Kramer, David Ham, Matthew Piggott 


Numerical modelling frequently involves a diagnostic quantity of interest (QoI) - often of greater importance than the PDE solution - which we seek to accurately approximate. In the case of coastal ocean modelling the power output of a tidal turbine farm is one such example. Goal-oriented error estimation and mesh adaptation can be used to provide meshes which are well-suited to achieving this goal, using fewer computational resources than required by other methods, such as uniform refinement.

A mixed discontinuous/continuous Galerkin approach is applied to solve the nonlinear shallow water equations within the Thetis coastal ocean finite element model. An implementation of goal-oriented mesh adaptation is outlined, including an error estimate which takes account of the discontinuities in the discrete solution and a method for approximating the adjoint error. Results are presented for simulations of two model tidal farm configurations. Convergence analysis indicates that the anisotropic goal-oriented adaptation strategy yields meshes which permit accurate QoI estimation using fewer computational resources than uniform refinement.




Applied Mathematics, Computer Sciences, Engineering, Non-linear Dynamics, Numerical Analysis and Computation, Numerical Analysis and Scientific Computing, Partial Differential Equations, Physical Sciences and Mathematics


Discontinuous Galerkin, Adjoint methods, Firedrake, Mesh adaptation, Tidal turbine modelling


Published: 2019-12-31 12:45

Last Updated: 2020-07-28 16:24

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