An-Najah Staff

In this article we focus our attention on the finite element error analysis for a problem involving both conductive and radiative heat transfer. We sketch the main steps of the analysis by stating the required a priori estimates and the final estimates. The proof for the estimate of the error due to approximation of the geometry is also presented. We prove an abstract estimate for the discretization error in a polygonal domain and combine it to the geometric estimate to yield the final error estimate. A concrete inverse monotone numerical method using view factors is analyzed using the abstract estimates.

We present a computationally efficient algorithm which combines the finite element method with Pade approximation. The combination is used to solve the problem of transverse magnetic and transverse electric scattering from homogeneous lossy dielectric cylinders over a continuous range of the complex permittivity variable by requiring the finite element solution only at a single complex permittivity value. The proposed method is based on (1) assuming a power series expansion for the unknown solution vector, the excitation vector, and the system matrix, (2) substituting this into the system matrix equation, and (3) finding the recursion relation for the solution vectors.