Convergence of a numerical method in mathematical spontaneous potential well-logging
Yi Zhou, Zhijie Cai · European Journal of Applied Mathematics · 1996
Spontaneous potential well-logging is an important technique in petroleum exploitation. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on interfaces. At the joint points of the interfaces, the jumps of the spontaneous potential do not, in general, satisfy the compatibility condition. It turns out that it is impossible to find a piecewiseH1solution to the problem, and the standard finite element method cannot be applied to get an approximate solution. In this paper, by means of a new method, we prove that the problem exists a unique piecewise solution for somep< 2. We give an estimate for the solution as well. This allows us to prove the convergence of a numerical scheme proposed in [3].