Anisotropic Goal-Oriented Error Analysis For A Third-Order Accurate Ceno Euler Discretization

In this paper, a central essentially non-oscillatory approximation based on a quadratic polynomial reconstruction is considered for solving the unsteady 2D Euler equations. The scheme is third-order accurate on irregular unstructured meshes. The paper concentrates on a method for a metric-based goal-oriented mesh adaptation. For this purpose, an a priori error analysis for this central essentially non-oscillatory scheme is proposed. It allows us to get an estimate depending on the polynomial reconstruction error. As a third-order error is not naturally expressed in terms of a metric, we propose a least-square method to approach a third-order error by a quadratic term. Then an optimization problem for the best mesh metric is obtained and analytically solved. The resulting mesh optimality system is discretized and solved using a global unsteady fixed-point algorithm. The method is applied to an acoustic propagation benchmark.