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Title: An anisotropic hp-adaptation framework for ultraweak discontinuous Petrov-Galerkin formulations
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 â„Ž-and đť‘ť-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.  more » « less
Award ID(s):
2103524
PAR ID:
10633358
Author(s) / Creator(s):
; ;
Publisher / Repository:
Elsevier
Date Published:
Journal Name:
Computers & Mathematics with Applications
Volume:
167
Issue:
C
ISSN:
0898-1221
Page Range / eLocation ID:
315 to 327
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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