A new patch up technique for elliptic partial differential equation with irregularities
Singh, Suruchi 1Li, Zhilin 2Singh, Swarn1
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作者信息
1. Univ Delhi
2. North Carolina State Univ
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Abstract
This paper presents a new technique based on a collocation method using cubic splines for second order elliptic equation with irregularities in one dimension and two dimensions. The differential equation is first collocated at the two smooth sub domains divided by the interface. We extend the sub domains from the interior of the domain and then the scheme at the interface is developed by patching them up. The scheme obtained gives the second order accurate solution at the interface as well as at the regular points. Second order accuracy for the approximations of the first order and the second order derivative of the solution can also be seen from the experiments performed. Numerical experiments for 2D problems also demonstrate the second order accuracy of the present scheme for the solution u and the derivatives u(x), u(xx) and the mixed derivative u(xy). The approach to derive the interface relations, established in this paper for elliptic interface problems, can be helpful to derive high order accurate numerical methods. Numerical tests exhibit the super convergent properties of the scheme. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
Key words
Elliptic partial differential equation/Interface/Jump conditions/Cubic spline collocation/Irregularities/Patch up technique/INTERFACE PROBLEMS
NSTL
Elsevier