Abstract: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.
From: So-Hsiang Chou [view email]
[v1]
Sat, 9 May 2026 18:16:53 UTC (49 KB)
[v2]
Tue, 23 Jun 2026 05:21:17 UTC (52 KB)
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