An Estimate for the Discrete Derivative Green's Function for the 4D Variable Coefficient Elliptic Equation
In this paper, definitions of the regularized derivative Green's function partial derivative(Z,l)G(Z)* and the discrete derivative Green's function partial derivative(Z,l)G(Z)(h) in four dimensions are first given. With complicated arguments, the W-1,W-1-seminorm estimate for partial derivative(Z,l)G(Z)* is then derived. Finally, applying the triangle inequality and the error estimate of the finite element approximation results in the W-1,W-1-seminorm estimate with order O(vertical bar In h vertical bar(G/4)) for partial derivative(Z,l)G(Z)(h).
discrete derivative green's function regularized derivative green's function w-1,w-1-seminorm estimate