A new nonconforming finite element with a conforming finite element approximation for a coupled continuum pipe‐flow/Darcy model in Karst aquifers |
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| Authors: | Wei Liu Xiaohan Long |
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| Affiliation: | School of Mathematics and Statistics Science, Ludong University, Yantai, China |
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| Abstract: | Numerical method is considered for a coupled continuum pipe‐flow/Darcy model describing flow in porous media with an embedded conduit pipe. A new nonconforming element is constructed to solve the Darcy equation on porous matrix. The existence and uniqueness of the approximation solution are deduced. Optimal error estimates are obtained in  and  norms. Some numerical examples show the accuracy and efficiency of the presented method. With the same number of nodal‐points and the same amount of computation, the results using the new nonconforming element are much better than those by both  conforming element and Wilson nonconforming element on the same mesh. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 778–798, 2016 |
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| Keywords: | coupled continuum pipe‐flow/Darcy model Karst aquifers nonconforming finite element numerical analysis |
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