Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Post-Processing Unstructured Discontinuous Galerkin Fields

2015 ◽  
Author(s):  
Robert M. Kirby
Keyword(s):  
Discontinuous Galerkin ◽  
Post Processing

Superconvergent discontinuous Galerkin methods for nonlinear parabolic initial and boundary value problems

2019 ◽  
Vol 27 (3) ◽  
pp. 183-202 ◽  
Author(s):  
Sangita Yadav ◽  
Amiya K. Pani
Keyword(s):  
Discontinuous Galerkin ◽  
Order Of Convergence ◽  
Discontinuous Galerkin Methods ◽  
Time Variable ◽  
Parabolic Problems ◽  
Galerkin Methods ◽  
Post Processing ◽  
Spatial Direction ◽  
Piecewise Polynomials ◽  
Nonlinear Parabolic

Abstract In this article, we discuss error estimates for nonlinear parabolic problems using discontinuous Galerkin methods which include HDG method in the spatial direction while keeping time variable continuous. When piecewise polynomials of degree k ⩾ 1 are used to approximate both the potential as well as the flux, it is shown that the error estimate for the semi-discrete flux in L∞(0, T; L2)-norm is of order k + 1. With the help of a suitable post-processing of the semi-discrete potential, it is proved that the resulting post-processed potential converges with order of convergence $\begin{array}{} \displaystyle O\big(\!\sqrt{{}\log(T/h^2)}\,h^{k+2}\big) \end{array}$ in L∞(0, T; L2)-norm. These results extend the HDG analysis of Chabaud and Cockburn [Math. Comp. 81 (2012), 107–129] for the heat equation to non-linear parabolic problems.

APPLYING THE ISF TECHNOLOGY TO PRODUCE THE CAR PART MODELS

2010 ◽  
Vol 13 (4) ◽  
pp. 91-98
Author(s):  
Tuan Dinh Phan ◽  
Binh Thien Nguyen ◽  
Dien Khanh Le ◽  
Phuong Hoang Pham
Keyword(s):  
Rapid Prototyping ◽  
Incremental Sheet Forming ◽  
Cad Model ◽  
Post Processing ◽  
Technological Parameters ◽  
Batch Production ◽  
Complex Products ◽  
3D Cad ◽  
Real Size ◽  
Single Batch

The paper presents an application the research results previously done by group on the influence of technological parameters to the deformation angle and finish surface quality in order to choose technology parameters for the incremental sheet forming (ISF) process to produce products for the purpose of rapid prototyping or single-batch production, including all steps from design and process 3D CAD model, calculate and select the technological parameters, setting up manufacturing and the stage of post-processing. The samples formed successfully showed high applicability of this technology to practical work, the complex products with the real size can be produced in industries: automotive, motorcycle, civil...

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