Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 131, Issue -, Pages 54-67Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2022.11.016
Keywords
Surface PDEs; Immersed interface method; Interface problems; Finite element method
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In this article, an immersed finite element approach is introduced for solving interface problems of elliptic PDEs on curved surfaces. The approach avoids the need for complicated body-fitting surface grids and can efficiently capture sharp solutions across the interface. The proposed method performs substantially superior to the conventional surface finite element method, as verified by numerical examples.
In this article, an immersed finite element approach is presented for solving interface problems of elliptic PDEs on curved surfaces. Such surface PDEs involve discontinuities in the coefficients. The immersed surface finite element method can avoid complicated body-fitting surface grids generating. The construction of immersed surface finite element space uses generic linear basis functions over non-interface components while the piecewise linear basis functions satisfying jump conditions are applied on interface elements. Thus the proposed approach can efficiently capture the sharp solutions across the interface, and performs substantially superior to the conventional surface finite element method. The error estimate of energy norm is shown. Numerical examples verify the superiorities of the presented method.
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