# Wedge product between relative de Rham cohomology and de Rham cohomology on a subspace

Under appropriate conditions on $$U\subset X$$ (what are they?), is there a well-defined wedge product $$\wedge: H^k(X,\overline U)\oplus H^l(X\setminus U)\to H^{k+l}(X,\overline U),$$ and if so, is there a name for it? What is the canonical way to define it?