Fixed mesh finite element approximations to a free boundary problem for an elliptic equation with an oblique derivative boundary condition

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Abstract

A method for approximating the solution of an elliptic equation with an oblique derivative on a curved boundary using an unfitted finite element mesh is presented and analysed. It is shown that the method retains the order of accuracy of the fitted mesh finite element method. A similar result is obtained for a variational inequality. The usefulness of this approach is then demonstrated by using it to approximate the solution of a free boundary problem on a fixed mesh. © 1985.

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Barrett, J. W., & Elliott, C. M. (1985). Fixed mesh finite element approximations to a free boundary problem for an elliptic equation with an oblique derivative boundary condition. Computers and Mathematics with Applications, 11(4), 335–345. https://doi.org/10.1016/0898-1221(85)90058-6

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