A CLASS OF INTERPOLATION-INVARIANT SCHEMES FOR THE NUMERICAL SOLUTION OF A HEAT CONDUCTION EQUATION

V. E. Troshchiev, R. M. Shagaliev
Vant. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1983. Вып.3. С. 73-76.

      A class of schemes referred to as interpolation-invariant or J-schemes is proposed for heat conduction equations. Mesh temperatures are set at polygon nodes. The J-scheme feature is that after a double temperature interpolation, that is from nodes to cell centers and vice versa, the solution on the mesh nodes remains unchanged. These schemes are of some interest in terms of solving heat conduction equations together with other equations where mesh functions to be found are introduced at polygon centers.