We consider a numerical method for the Volterra-Fredholm integral equation
of the first kind corresponding to the Dirichlet problem
of heat conduction in a solid with piecewise Lyapunov surface
with corners and edges. To approximate the ill-posed boundary integral
equation we adopt the Galerkin method using boundary finite element
and one-dimensional finite element in the time variable.
We show the convergence property and the stability of the
semi-discretized approximate solution using
boundary finite elements. We estimate the error bound for
the full-discretized approximate solution.