Superconvergence of Modified Nonconforming Cut Finite Element Method for Elliptic Problems

Xiaoxiao He and Fei Song ()
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Xiaoxiao He: School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Fei Song: College of Science, Nanjing Forestry University, Nanjing 210037, China

Mathematics, 2024, vol. 12, issue 16, 1-9

Abstract: In this work, we aim to explore the superconvergence of a modified nonconforming cut finite element method with rectangular meshes for elliptic problems. Boundary conditions are imposed via the Nitsche’s method. The superclose property is proven for rectangular meshes. Moreover, a postprocessing interpolation operator is introduced, and it is proven that the postprocessed discrete solution converges to the exact solution, with a superconvergence rate O ( h 3 / 2 ) . Finally, numerical examples are provided to support the theoretical analysis.

Keywords: superconvergence; modified nonconforming cut finite element; rectangular meshes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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