Goal-Oriented Anisotropic hp-Adaptive Discontinuous Galerkin Method for the Euler Equations

Abstrakt

We deal with the numerical solution of the compressible Euler equations with the aid of the discontinuous Galerkin (DG) method with focus on the goal-oriented error estimates and adaptivity. We analyse the adjoint consistency of the DG scheme where the adjoint problem is not formulated by the differentiation of the DG form and the target functional but using a suitable linearization of the nonlinear forms.

Furthermore, we present the goal-oriented anisotropic hp-mesh adaptation method for the Euler equations. The theoretical results are supported by numerical experiments.

Klíčová slova

• Euler equations
• Discontinuous Galerkin method
• Target functional
• Adjoint consistency
• Anisotropic hp-mesh adaptation