A Special Corner Element for Solving Heat Conduction Problems

A hybrid Trefftz finite element method is proposed for solving heat conduction problems in a domain with concave or convex angles. In this method, two temperature fields are independently assumed, one of which is the intra-element field defined inside the element and the other is the frame field defined on the boundary. The corner effects embed in the truncated complete solutions which are used to construct the internal interpolation function for approximating the intra-element field. It is able to accurately analyze the problems with particular corners. The key characteristics lie in the finite element formulation which is evaluated along the element boundary. Compared with the conventional FEM, the corner element does not lose any accuracy by using a small number of elements. Numerical examples demonstrate that the proposed method exhibits low sensitivity to mesh distortion. Compared with ABAQUS, the proposed method also exhibits higher accuracy and a faster convergence rate.