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

by   Ankit Chakraborty, et al.

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


page 12

page 17

page 18

page 20


An Anisotropic hp-Adaptation Framework for Ultraweak Discontinuous Petrov-Galerkin Formulations

In this article, we present a three-dimensional anisotropic hp-mesh refi...

Optimal approximation spaces for discontinuous Petrov-Galerkin finite element methods

Certain Petrov-Galerkin schemes are inherently stable formulations of va...

A class of Discontinuous Galerkin methods for nonlinear variational problems

In the context of Discontinuous Galerkin methods, we study approximation...

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

In the context of Discontinuous Galerkin Spectral Element Methods (DGSEM...

Medical Image Registration using optimal control of a linear hyperbolic transport equation with a DG discretization

Patient specific brain mesh generation from MRI can be a time consuming ...

Please sign up or login with your details

Forgot password? Click here to reset