Speaker
Description
We introduce a novel unfitted finite element method for elliptic problems posed on domains with embedded inclusions. The proposed approach extends the standard Fictitious Domain framework by enforcing a smooth extension of the solution inside the fictitious region. This feature allows the method to attain optimal convergence rates in settings where classical Fictitious Domain formulations may exhibit reduced accuracy. The method is simple to implement, does not require any enrichment of the finite
element space, and provides an excellent trade-off between computational cost and accuracy. We analyze the method within the framework of generalized saddle-point problems, establishing the well-posedness of both the continuous and discrete formulations. An inexact integration strategy is employed for the coupling terms, and analytical estimates for the resulting quadrature errors are derived. Although the inexact integration introduces additional lower-order error terms for continuous piecewise linear finite elements, numerical experiments in two and three dimensions show that these effects are not dominant at practical refinement levels, and optimal convergence rates are observed.