The Fourier finite element method for the corner singularity expansion of the Heat equation
Near the non-convex vertex the solution of the Heat equation is of the form u = ( c ? E ) ? r ? / ? sin ( ? ? ? ) + w , w ? L 2 ( R + ; H 2 ) , where c c is the stress intensity function of the time variable t t , ? ? the convolution, E ( x , t ) = r e ? r 2 / 4 t / 2 ? t 3 , ? ? a cutoff function and ? ? the opening angle of the vertex. In this paper we use the Fourier finite element method for approximating the stress intensity function c c and the regular part w w , and derive the error estimates depending on the regularities of c c and w w . We give some numerical examples, confirming the derived convergence rates.
fourier finite element method corner singularity error estimate