AbstractWe investigate a weak space-time formulation of the
heat equation and its use for the construction of a numerical scheme.
The formulation is based on a known weak space-time formulation, with
the difference that a pointwise component of the solution, which in
other works is usually neglected, is now kept. We investigate the role
of such a component by first using it to obtain a pointwise bound on
the solution and then deploying it to construct a numerical scheme.
The scheme obtained, besides being quasi-optimal in the ${L^{2}}$ sense, is also
pointwise superconvergent in the temporal nodes. We prove a priori error estimates and we present numerical experiments to empirically support our findings.
Role of Graphs in Blending Physical and Mathematical Meaning of Partial Derivatives in the Context of the Heat Equation
