Pseudo‐transparent boundary conditions for the diffusion equation. Part I
Patrick Joly, Jean-Claude Nédélec · Mathematical Methods in the Applied Sciences · 1989
Abstract In this article, we introduce and study a family of artificial boundary conditions for the diffusion equation. These conditions are local in time and non‐local in space. We describe the principle of the approximation, show that the corresponding approximate problems are mathematically well‐posed and give convergence results, as well as error estimates, of the approximate solution to the exact one.