INFLUENCE OF IRREGULAR TRIANGULATION ON THE FINITE ELEMENT CONVERGENCE
Tian Min · Journal of Petrochemical Universities · 2004
The mesh dissection is a proceeding study subject in the finite element theory at present. With the super computer developing continuously, it is possible to do large-scale scientific computation. However, the mesh dissection in the classical finite element theory still needs to be given more attention. FENG Kang proved the error estimates for linear Lagrange interpolation based on the triangular element. Strang G pointed out that it wasn't permitted to use obtuse angle element in the triangulation. Combined with the above two conclusions, there are two kinds of dissections, one is acute angle triangulation, the other is obtuse angle triangulation. The results for the acute angle triangulation will have important meaning and profound influences on the real problems. First, the property of 2’degree Lagrange interpolation under acute angle element and obtuse angle element is analyzed, and then the finite element error estimates to the Poisson boundary problem in the plane polygon domain is proved. The analysis conclusion is also verified by the example of numerical computation. The definite theoretical basis is given for the computation reality of acute angle triangulation to a certain extent.