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Volume 12, Issue 4
New Mixed Finite Volume Spaces for Elliptic Problems on Parallelepiped

Ji Hyun Kim

DOI: 10.4208/aamm.OA-2018-0239

Adv. Appl. Math. Mech., 12 (2020), pp. 959-971.

Published online: 2020-06

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  • Abstract

In this paper, we define a new nonconforming finite element space on parallelepiped. Using our new nonconforming space and a vector part of  Kim-Kwak mixed finite element space, we suggest a new class of higher order mixed finite volume method. We show that the mixed finite volume methods can be implemented by solving the primal problem with our new nonconforming finite element methods for the pressure variable. And we can obtain the velocity variable by local recovery technique. An optimal error analysis is given and also numerical results are presented to support our analysis.

  • Keywords

Mixed finite volume methods, nonconforming finite element methods, mixed finite element methods, error analysis.

  • AMS Subject Headings

65N15, 65N30, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

kimjh@hnu.kr (Ji Hyun Kim)

  • BibTex
  • RIS
  • TXT
@Article{AAMM-12-959, author = {Hyun Kim , Ji}, title = {New Mixed Finite Volume Spaces for Elliptic Problems on Parallelepiped}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {4}, pages = {959--971}, abstract = {

In this paper, we define a new nonconforming finite element space on parallelepiped. Using our new nonconforming space and a vector part of  Kim-Kwak mixed finite element space, we suggest a new class of higher order mixed finite volume method. We show that the mixed finite volume methods can be implemented by solving the primal problem with our new nonconforming finite element methods for the pressure variable. And we can obtain the velocity variable by local recovery technique. An optimal error analysis is given and also numerical results are presented to support our analysis.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0239}, url = {http://global-sci.org/intro/article_detail/aamm/16935.html} }
TY - JOUR T1 - New Mixed Finite Volume Spaces for Elliptic Problems on Parallelepiped AU - Hyun Kim , Ji JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 959 EP - 971 PY - 2020 DA - 2020/06 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2018-0239 UR - https://global-sci.org/intro/article_detail/aamm/16935.html KW - Mixed finite volume methods, nonconforming finite element methods, mixed finite element methods, error analysis. AB -

In this paper, we define a new nonconforming finite element space on parallelepiped. Using our new nonconforming space and a vector part of  Kim-Kwak mixed finite element space, we suggest a new class of higher order mixed finite volume method. We show that the mixed finite volume methods can be implemented by solving the primal problem with our new nonconforming finite element methods for the pressure variable. And we can obtain the velocity variable by local recovery technique. An optimal error analysis is given and also numerical results are presented to support our analysis.

Ji Hyun Kim. (2020). New Mixed Finite Volume Spaces for Elliptic Problems on Parallelepiped. Advances in Applied Mathematics and Mechanics. 12 (4). 959-971. doi:10.4208/aamm.OA-2018-0239
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