Abstract
A new characteristic/Lagrange Galerkin finite element method using an Hermitian type element, named Hermitian characteristic Galerkin (HCG) method, is proposed for solving advection diffusion problems. Using the Hermitian type element can improve accuracy of the characteristic Galerkin finite element method. A composed function for each element included in the formulation of the characteristic Galerkin finite element method can approximate a polynomial function by constructing the Hermitian type element in upwind position, and it is possible to perform integration of the term included in the composed function analytically. The 10-DOF Hermitian type triangular element which consists of cubic polynomials given by function values and first order derivatives on each vertex and a function value on barycenter of a triangle is used in the two dimensional calculation. Two numerical experiments for the two dimensional advection diffusion equation are investigated and the results show the effectiveness of the present method by evaluating the computational accuracy.
