A scalar interface reduction for nonlinear interface problems
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910205622616064 |
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| author | Chou, So-Hsiang |
| author_facet | Chou, So-Hsiang |
| contents | We study finite element approximations of elliptic and parabolic interface problems with discontinuous coefficients and nonlinear jump conditions. We introduce a scalar interface reduction in which the solution is decomposed into a continuous component and a unit-jump response mode. This representation isolates the interface nonlinearity into a single scalar variable while the bulk problem remains linear.
From this perspective, the nonlinear interface condition is reduced to a scalar nonlinear equation, which may be interpreted as a nonlinear Schur complement associated with the interface degree of freedom. The resulting formulation leads to a simple computational procedure consisting of linear solves combined with a low-dimensional nonlinear update.
Numerical results for representative elliptic and parabolic problems confirm second-order accuracy for interface quantities and demonstrate the effectiveness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09102 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A scalar interface reduction for nonlinear interface problems Chou, So-Hsiang Numerical Analysis 65N30, 65N12 We study finite element approximations of elliptic and parabolic interface problems with discontinuous coefficients and nonlinear jump conditions. We introduce a scalar interface reduction in which the solution is decomposed into a continuous component and a unit-jump response mode. This representation isolates the interface nonlinearity into a single scalar variable while the bulk problem remains linear. From this perspective, the nonlinear interface condition is reduced to a scalar nonlinear equation, which may be interpreted as a nonlinear Schur complement associated with the interface degree of freedom. The resulting formulation leads to a simple computational procedure consisting of linear solves combined with a low-dimensional nonlinear update. Numerical results for representative elliptic and parabolic problems confirm second-order accuracy for interface quantities and demonstrate the effectiveness of the proposed approach. |
| title | A scalar interface reduction for nonlinear interface problems |
| topic | Numerical Analysis 65N30, 65N12 |
| url | https://arxiv.org/abs/2605.09102 |