Application of the modified method of finite elements to identification of temperature of a body heated with a moving heat source

A transient 2-dimensional problem of heat flow with a moving heat source is considered. It is assumed that the heat source is moving along one of the sides of a rectangle with a constant velocity. The unknown is the temperature distribution in a flat rectangular area. The paper presents an approximate solution which is based on the finite element method with a modified basis function. The space-time basis functions are combinations of heat polynomials which strictly satisfy the heat equation. Cartesian coordinates were used to solve the problem.