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| 005 | 20260901030406.0 | ||
| 008 | 250101s2020 xx o 000 0 eng d | ||
| 100 | 1 | _aHengguang Li | |
| 245 | 1 | 0 | _aA $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain |
| 264 | 1 |
_barXiv _c2020 |
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| 336 | _atext | ||
| 338 | _aonline resource | ||
| 520 | _aIn this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different from the usual mixed method that leads to two Poisson problems but only applies to convex domains, the proposed decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and non-convex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulted system. In addition, we derive the optimal error estimates for the numerical solution on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings. | ||
| 506 | 0 | _aOpen access — freely available to read. | |
| 856 | 4 | 0 |
_uhttps://arxiv.org/pdf/2012.12374v1 _yRead the full paper (PDF) |
| 942 | _cERES | ||
| 999 |
_c701 _d701 |
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