Adjoint-based anisotropic mesh adaptation for discontinuous Galerkin methods using a continuous mesh model
In this paper we propose an adjoint-based mesh optimization method for conservation laws, which may be used with any numerical method based on piecewise polynomials. The method uses a continuous mesh framework, similar to that proposed in [19], where a global optimization scheme was formulated with respect to the error in the numerical solution, measured in any Lq norm. The novelty of the present work is the extension to more general optimization targets. Here, any solution-dependent functional, which is compatible with an adjoint equation, may be the target of the continuous-mesh optimization. We present the rationale behind the formulation of the optimization problem, with particular emphasis on the continuous mesh model, and the relevant adjoint-based error estimate. We also present numerical results, demonstrating the viability of the scheme.
