Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface
Published in ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2025
The objective of this work is to study a diffusion equation with non-standard transmission conditions, which include discontinuities and the Ventcel boundary conditions at the interface. To handle jumps and means of the flux and test-functions, we use broken Sobolev spaces. We present a Nitsche finite element approach and compare it with a discontinuous Galerkin method. Consistency, stability and a priori error estimates are proven and numerically verified.
Recommended citation: D. Capatina, F. Caubet, M. Dambrine, and R. Zelada. Nitsche extended finite element method of a Ventcel transmission problem with discontinuities at the interface. ESAIM Math. Model. Numer. Anal., 59(2):999–1021, 2025.
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