Superconvergence of a Nonconforming Interface Penalty Finite Element Method for Elliptic Interface Problems
In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively. In this paper, a nonconforming interface penalty finite element method (NIPFEM) based on body-fitted meshes...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-05-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/5/364 |
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| Summary: | In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively. In this paper, a nonconforming interface penalty finite element method (NIPFEM) based on body-fitted meshes is explored for elliptic interface problems, which allows us to use different meshes in different sub-domains separated by the interface. A nonconforming finite element method based on rectangular meshes is studied and the supercloseness property between the gradient of the numerical solution and the gradient of the interpolation of the exact solution is proven for both symmetric NIPFEM and nonsymmetric NIPFEM. Then, the global superconvergence rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>h</mi><mi>i</mi><mstyle scriptlevel="0" displaystyle="true"><mfrac><mn>3</mn><mn>2</mn></mfrac></mstyle></msubsup><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> between the postprocessed numerical solution of NIPFEM and the exact solution is derived by using an interpolation postprocessing technique. Numerical examples are carried out to demonstrate the theoretical results. |
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| ISSN: | 2075-1680 |