THE MAXIMUM ANGLE CONDITION IN THE FINITE-ELEMENT METHOD FOR MONOTONEPROBLEMS WITH APPLICATIONS IN MAGNETOSTATICS

The finite element method for an elliptic equation with discontinuous coefficients (obtained for the magnetic potential from Maxwell's equat ions) is analyzed in the union of closed domains the boundaries of whi ch form a system of three circles with the same centre. As the middle domain is very narrow the triangulations obeying the maximum angle con dition are considered. In the case of piecewise linear trial functions the maximum rate of convergence O(h) in the norm of the space H-1(Ome ga(h)) is proved under the following conditions: 1. the exact solution u is an element of H-1(Omega) is piecewise of class H-2; 2. the famil y of subtriangulations (J(h)(A)) Of the narrow subdomain Omega(A) sati sfies the maximum angle condition expressed by relation (38). The pape r extends the results of [24].