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

09/01/2023
by   Ankit Chakraborty, et al.
0

In this article, we present a three-dimensional anisotropic hp-mesh refinement strategy for ultraweak discontinuous Petrov–Galerkin (DPG) formulations with optimal test functions. The refinement strategy utilizes the built-in residual-based error estimator accompanying the DPG discretization. The refinement strategy is a two-step process: (a) use the built-in error estimator to mark and isotropically hp-refine elements of the (coarse) mesh to generate a finer mesh; (b) use the reference solution on the finer mesh to compute optimal h- and p-refinements of the selected elements in the coarse mesh. The process is repeated with coarse and fine mesh being generated in every adaptation cycle, until a prescribed error tolerance is achieved. We demonstrate the performance of the proposed refinement strategy using several numerical examples on hexahedral meshes.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset