| On the convergence of finite difference scheme for elliptic equation with coefficients containing Dirac distribution |
| Boško S. Jovanović, Lubin G. Vulkov |
Abstract First boundary value problem for elliptic equation with youngest coefficient containing Dirac distribution concentrated on a smooth curve is considered. For this problem a finite difference scheme on a special quasiregular grid is constructed. The finite difference scheme converges in discrete $W_2^1$ norm with the rate $O(h^{3/2})$. Convergence rate is compatible with the smoothness of input data.
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Keywords: Boundary value problem, generalized solution, finite differences, rate of convergence. |
MSC: 65N15 |
Pages: 115$-$123 |
Volume 56 , Issue 3$-$4 , 2004 |
