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Anisotropic Quasi-Wilson Element with Conforming Finite Element Approximation for Coupled Continuum Pipe-Flow/Darcy Model in Karst Aquifers

    Wei Liu Affiliation
    ; Jintao Cui Affiliation

Abstract

This paper presents a numerical method for solving systems of partial differential equations describing flow in porous media with an embedded and inclined conduit pipe. This work considers a coupled continuum pipe-flow/Darcy model. The numerical schemes presented are based on combinations of the quasi-Wilson element on anisotropic mesh and the conforming finite element on regular mesh. The existence and uniqueness of the approximation solution are obtained. Optimal error estimates in both L2 and H1 norms are obtained independent of the regularity condition on the mesh. Numerical examples show the accuracy and efficiency of the proposed scheme.

Keyword : Karst aquifers, quasi-Wilson element, anisotropic mesh, coupled continuum pipe-flow/Darcy model, numerical analysis

How to Cite
Liu, W., & Cui, J. (2016). Anisotropic Quasi-Wilson Element with Conforming Finite Element Approximation for Coupled Continuum Pipe-Flow/Darcy Model in Karst Aquifers. Mathematical Modelling and Analysis, 21(4), 431-449. https://doi.org/10.3846/13926292.2016.1175388
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Jun 23, 2016
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This work is licensed under a Creative Commons Attribution 4.0 International License.