Truncation Error Estimation in the p-Anisotropic Discontinuous Galerkin Spectral Element Method

摘要: In the context of discontinuous Galerkin spectral element methods (DGSEM), $$\tau $$ -estimation has been successfully used for p-adaptation algorithms. This method estimates truncation error representations with different polynomial orders using solution on a reference mesh relatively high order. this paper, we present novel anisotropic estimator derived from procedure traditional DGSEM. We exploit tensor product basis properties numerical to design where total is calculated as sum its directional components. show that new cheaper evaluate than previous implementations and it obtains more accurate extrapolations higher order mesh. The robustness allows performing strategy coarser solutions, thus further reducing computational cost. proposed validated manufactured solutions in test case compressible Navier–Stokes equations.