Adaptive space-time BEM for the heat equation with Neumann boundary conditions

We consider the space-time boundary element method (BEM) for the heat equation with prescribed initial and Neumann data.

We propose a weighted-residual a posteriori error estimator that is an upper bound for the unknown BEM error.

The possibly locally refined meshes are assumed to be parabolically scaled prismatic, i.e., their elements are tensor-products $J\times K$ of elements in time $J$ and space $K$ with $|J| \eqsim \text{diam}(K)^2$.

In the considered numerical experiments on two-dimensional domains in space, an adaptive algorithm steered by the derived estimator yields significantly faster convergence compared to uniform refinement, achieving near-optimal rates even in the presence of strong singularities.