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Volume 12, Issue 2
A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems

Yuanyuan Zhang & Min Yang

DOI: 10.4208/aamm.OA-2019-0012

Adv. Appl. Math. Mech., 12 (2020), pp. 564-578.

Published online: 2020-01

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  • Abstract

In this paper, we construct and analyze the a posteriori error estimators for any order finite volume methods (FVMs) for solving the elliptic boundary value problems in $R^2$. We shall prove that the a posteriori error estimators yield the global upper and local lower bounds for the $H^1$-norm error of the corresponding FVMs. So that the a posteriori error estimators are equivalent to the true errors in a certain sense. Lots of numerical experiments are performed to illustrate the theoretical results.

  • Keywords

Any order finite volume methods, a posteriori error estimate.

  • AMS Subject Headings

65N30, 65N12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yy0dd@126.com (Yuanyuan Zhang)

yang@ytu.edu.cn (Min Yang)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-564, author = {Zhang , Yuanyuan and Yang , Min}, title = {A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {2}, pages = {564--578}, abstract = {

In this paper, we construct and analyze the a posteriori error estimators for any order finite volume methods (FVMs) for solving the elliptic boundary value problems in $R^2$. We shall prove that the a posteriori error estimators yield the global upper and local lower bounds for the $H^1$-norm error of the corresponding FVMs. So that the a posteriori error estimators are equivalent to the true errors in a certain sense. Lots of numerical experiments are performed to illustrate the theoretical results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0012}, url = {http://global-sci.org/intro/article_detail/aamm/13634.html} }
TY - JOUR T1 - A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems AU - Zhang , Yuanyuan AU - Yang , Min JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 564 EP - 578 PY - 2020 DA - 2020/01 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0012 UR - https://global-sci.org/intro/article_detail/aamm/13634.html KW - Any order finite volume methods, a posteriori error estimate. AB -

In this paper, we construct and analyze the a posteriori error estimators for any order finite volume methods (FVMs) for solving the elliptic boundary value problems in $R^2$. We shall prove that the a posteriori error estimators yield the global upper and local lower bounds for the $H^1$-norm error of the corresponding FVMs. So that the a posteriori error estimators are equivalent to the true errors in a certain sense. Lots of numerical experiments are performed to illustrate the theoretical results.

Zhang , Yuanyuan and Yang , Min. (2020). A Posteriori Error Analysis of Any Order Finite Volume Methods for Elliptic Problems. Advances in Applied Mathematics and Mechanics. 12 (2). 564-578. doi:10.4208/aamm.OA-2019-0012
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