Smoothness-Increasing Accuracy-Conserving (SIAC) filters for derivative approximations of discontinuous Galerkin (DG) solutions over nonuniform meshes and near boundaries

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:294

Article

Li, X.¹  Ryan, J. K.²  Kirby, R. M.³  Vuik, C.¹ 

[1] Delft Univ Technol, Delft Inst Appl Math, Delft, Netherlands

[2] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

[3] Univ Utah, Sch Comp, Salt Lake City, UT USA

关键词: Discontinuous Galerkin method;    Post-processing;    SIAC filtering;    Superconvergence;    Nonuniform meshes;    Boundaries;   

DOI  :  10.1016/j.cam.2015.08.011

来源: Elsevier

【 摘 要 】

Accurate approximations for the derivatives are usually required in many application areas such as biomechanics, chemistry and visualization applications. With the help of Smoothness-Increasing Accuracy-Conserving (SIAC) filtering, one can enhance the derivatives of a discontinuous Galerkin solution. However, current investigations of derivative filtering are limited to uniform meshes and periodic boundary conditions, which do not meet practical requirements. The purpose of this paper is twofold: to extend derivative filtering to nonuniform meshes and propose position-dependent derivative filters to handle filtering near the boundaries. Through analyzing the error estimates for SIAC filtering, we extend derivative filtering to nonuniform meshes by changing the scaling of the filter. For filtering near boundaries, we discuss the advantages and disadvantages of two existing position-dependent filters and then extend them to position-dependent derivative filters, respectively. Further, we prove that with the position-dependent derivative filters, the filtered solutions can obtain a better accuracy rate compared to the original discontinuous Galerkin approximation with arbitrary derivative orders over nonuniform meshes. One- and two-dimensional numerical results are provided to support the theoretical results and demonstrate that the position-dependent derivative filters, in general, enhance the accuracy of the solution for both uniform and nonuniform meshes. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free