A Continuous hp-Mesh Model for Discontinuous Petrov-Galerkin Finite Element Schemes with Optimal Test Functions

11/21/2022
by   Ankit Chakraborty, et al.
0

We present an anisotropic hp-mesh adaptation strategy using a continuous mesh model for discontinuous Petrov-Galerkin (DPG) finite element schemes with optimal test functions, extending our previous work on h-adaptation. The proposed strategy utilizes the inbuilt residual-based error estimator of the DPG discretization to compute both the polynomial distribution and the anisotropy of the mesh elements. In order to predict the optimal order of approximation, we solve local problems on element patches, thus making these computations highly parallelizable. The continuous mesh model is formulated either with respect to the error in the solution, measured in a suitable norm, or with respect to certain admissible target functionals. We demonstrate the performance of the proposed strategy using several numerical examples on triangular grids. Keywords: Discontinuous Petrov-Galerkin, Continuous mesh models, hp- adaptations, Anisotropy

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset