Adjoint-based anisotropic mesh adaptation for Discontinuous Galerkin Methods Using a Continuous Mesh Model
Abstract
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, where a global optimization scheme was formulated with respect to the error in the numerical solution, measured in any $L^q$ 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.