IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v341y2019icp31-45.html
   My bibliography  Save this article

A numerical solution for the inhomogeneous Dirichlet boundary value problem on a non-convex polygon

Author

Listed:
  • Choi, Hyung Jun

Abstract

In this paper, we introduce an effective finite element scheme for the Poisson problem with inhomogeneous Dirichlet boundary condition on a non-convex polygon. Due to the corner singularities, the solution is composed of a singular part not belonging to the Sobolev space H2 and a smoother regular part. We first provide a generalized extraction formula for the coefficient of singular part, which is depending on the inhomogeneous boundary condition and the regular part. We then propose a stable finite element method for the regular part by the use of the derived formula. We show the H1 and L2 error estimates of the finite element solution for the regular part and the absolute error estimate of the approximation for the coefficient of singular part. Finally, we give some numerical examples to confirm the efficiency and reliability of the proposed method.

Suggested Citation

  • Choi, Hyung Jun, 2019. "A numerical solution for the inhomogeneous Dirichlet boundary value problem on a non-convex polygon," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 31-45.
    • Handle: RePEc:eee:apmaco:v:341:y:2019:i:c:p:31-45
    DOI: 10.1016/j.amc.2018.08.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318307252
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.08.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. World Bank, 2002. "Costa Rica : Social Spending and the Poor, Volume 1. Summary of Issues and Recommendations with Executive Summary," World Bank Publications - Reports 15330, The World Bank Group.
    2. Hernández-Hernández, M.E. & Kolokoltsov, V.N. & Toniazzi, L., 2017. "Generalised fractional evolution equations of Caputo type," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 184-196.
    3. Simon Levin & Anastasios Xepapadeas, 2021. "On the Coevolution of Economic and Ecological Systems," Annual Review of Resource Economics, Annual Reviews, vol. 13(1), pages 355-377, October.
    4. Hoang Ngoc Tuan, 2015. "Boundedness of a Type of Iterative Sequences in Two-Dimensional Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 234-245, January.
    5. Wang, Daojuan & Hain, Daniel S. & Larimo, Jorma & Dao, Li T., 2020. "Cultural differences and synergy realization in cross-border acquisitions," International Business Review, Elsevier, vol. 29(3).
    6. Zhou, H. & Uhlaner, L.M., 2009. "Knowledge Management in the SME and its Relationship to Strategy, Family Orientation and Organization Learning," ERIM Report Series Research in Management ERS-2009-026-ORG, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    7. Turpie, J.K. & Marais, C. & Blignaut, J.N., 2008. "The working for water programme: Evolution of a payments for ecosystem services mechanism that addresses both poverty and ecosystem service delivery in South Africa," Ecological Economics, Elsevier, vol. 65(4), pages 788-798, May.
    8. Koichi Hamada & Asahi Noguchi, 2005. "The Role of Preconceived Ideas in Macroeconomic Policy: Japan's Experiences in the Two Deflationary Periods," Working Papers 908, Economic Growth Center, Yale University.
    9. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    10. Dipak R. Pant, 2013. "Managing the global waste in the 21st century: As an anthropologist views it," LIUC Papers in Economics 263, Cattaneo University (LIUC).
    11. van der Laan, Gerard & Talman, Dolf & Yang, Zaifu, 2011. "Solving discrete systems of nonlinear equations," European Journal of Operational Research, Elsevier, vol. 214(3), pages 493-500, November.
    12. Richard ANKER, 2006. "Poverty lines around the world: A new methodology and internationally comparable estimates," International Labour Review, International Labour Organization, vol. 145(4), pages 279-307, December.
    13. X. F. Li & J. Z. Zhang, 2006. "Necessary Optimality Conditions in Terms of Convexificators in Lipschitz Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(3), pages 429-452, December.
    14. Popli, Manish & Akbar, Mohammad & Kumar, Vikas & Gaur, Ajai, 2016. "Reconceptualizing cultural distance: The role of cultural experience reserve in cross-border acquisitions," Journal of World Business, Elsevier, vol. 51(3), pages 404-412.
    15. Quah Chee-Heong, 2019. "China’s Dollar-linked Hong Kong during the Global Crisis," Apuntes del Cenes, Universidad Pedagógica y Tecnológica de Colombia, vol. 38(67), pages 95-121, February.
    16. Lan, Heng-you, 2021. "Approximation-solvability of population biology systems based on p-Laplacian elliptic inequalities with demicontinuous strongly pseudo-contractive operators," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    17. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2020. "On the difficulty of budget allocation in claims problems with indivisible items of different prices," ThE Papers 20/09, Department of Economic Theory and Economic History of the University of Granada..
    18. Slotnick, Susan A., 2011. "Order acceptance and scheduling: A taxonomy and review," European Journal of Operational Research, Elsevier, vol. 212(1), pages 1-11, July.
    19. Winfried Osthorst, 2020. "Tensions in Urban Transitions. Conceptualizing Conflicts in Local Climate Policy Arrangements," Sustainability, MDPI, vol. 13(1), pages 1-17, December.
    20. Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:341:y:2019:i:c:p:31-45. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.