In this paper, we propose a modified pollution error in r-h methods using singular elements. The algorithm based on the element pollution error indicator concentrate on boundary nodes. The singular shape function is used where an element includes a singular point. The conventional automatic mesh generation method with this special shape function is shown to be very effective in this algorithm. The boundary node relocation phase and node insertion method are used alternatively as before. It is shown that the suggested r-h version algorithm combined with singular elements converges more quickly than the conventional one.