This work presents an application of the hp- finite element formulation to solve the general non-linear heat conduction problem in a solid for cases involving heat sources and non-linear boundary conditions terms. The temperature field is semi-discretized in space with hierarchical basis functions formed using the orthogonal Legendre polynomials. The good approximation properties of the hp-finite element method are achieved here by the combined effect of the traditional mesh refinement together with the p-extension of the polynomial basis. Because the temperature field is continuous, the hp-formulation performs very well. The calculated temperature field converges much faster in the hp-version than the traditional h-refinement. In general, the h-refinement is used for regions with non-smooth solution and the p-extension for the smooth ones. This work also shows a systematic way to treat source terms and the possible non-linear natural boundary conditions present in the heat conduction equation by including them in the force vector of the discretized heat conduction equation.
|Publication status||Published - 1996|
|MoE publication type||D1 Article in a trade journal|