A new Petrov-Galerkin immersed finite element method for elliptic interface problems with non-homogeneous jump conditions. (English) Zbl 1517.65118
Summary: In this paper, we develop a Petrov-Galerkin immersed finite element method for solving elliptic interface problems in two and three dimensions. By introducing additional immersed finite element function on interface element, the non-homogeneous jump conditions can be dealt easily. In various test cases, including large jump in the coefficients and complex interfaces, the method can provide nearly second-order accuracy in the \(L^2\) and \(L^\infty\) norm.
MSC:
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
Keywords:
Cartesian mesh; immersed finite element; Petrov-Galerkin; three-dimensional interface problemsReferences:
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