Accurate gradient computations at interfaces using finite element methods

• Autorzy: Qin F. , Wang Z. , Ma Z. , Li Z.

Identyfikatory

DOI

10.1515/amcs-2017-0037

• Języki publikacji: EN

Abstrakty

EN

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is to get not only an accurate solution, but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea of Wheeler (1974). For 2D interface problems, the point is to introduce a small tube near the interface and propose the gradient as part of unknowns, which is similar to a mixed finite element method, but only at the interface. Thus the computational cost is just slightly higher than in the standard finite element method. We present a rigorous one dimensional analysis, which shows a second order convergence order for both the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface.

Słowa kluczowe

EN

elliptic interface problem; gradient flux computation; IFEM; mixed FE formulation; computational tube

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 3
• Strony: 527--537
• Opis fizyczny: Bibliogr. 31 poz., rys., tab., wykr.

Twórcy

autor

Qin F.

• School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, 210023 China

autor

Wang Z.

• Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA

autor

Ma Z.

• College of Resource and Environment, Wuhan University of Technology, Wuhan, 430070 China; China Institute of Water Resource and Hydropower Research (IWHR), Beijing, 100038 China

autor

Li Z.

• Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA

Bibliografia

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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).