Gorenstein Injective Projective and Flat (Pre)Covers

We prove that if the ring R is left noetherian and if the class GI of Gorenstein injective modules is closed under filtrations, then GI is precovering. We extend this result to the category of complexes. We also prove that when R is commutative noetherian and such that the character modules of Gorenstein injective modules are Gorenstein flat, the class of Gorenstein injective complexes is both covering and enveloping. This is the case when the ring is commutative noetherian with a dualizing complex. The second part of the paper deals with Gorenstein projective and flat complexes. We prove the existence of special Gorenstein projective precovers over commutative noetherian rings of finite Krull dimension.