Abstract
AbstractThis study presents a novel goal-oriented error estimate for the nonlinear shallow water equations solved using a mixed discontinuous/continuous Galerkin approach. This error estimator takes account of the discontinuities in the discrete solution and is used to drive two metric-based mesh adaptation algorithms: one which yields isotropic meshes and another which yields anisotropic meshes. An implementation of these goal-oriented mesh adaptation algorithms is described, including a method for approximating the adjoint error term which arises in the error estimate. Results are presented for simulations of two model tidal farm configurations computed using the Thetis coastal ocean model (Kärnä et al. in Geosci Model Dev 11(11):4359–4382, 2018). Convergence analysis indicates that meshes resulting from the goal-oriented adaptation strategies permit accurate QoI estimation using fewer computational resources than uniform refinement.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
General Earth and Planetary Sciences,General Physics and Astronomy,General Engineering,General Environmental Science,General Materials Science,General Chemical Engineering
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