OSPF doesn't use a mesh topology. All OSPF areas must connect to Area 0 (backbone area) because all traffic from one are to another area must travel through Area 0. This is a loop prevention mechanism.
An OSPF router knows about everything (routes routers, costs, etc.) in its own area. Areas separate and compartmentalize this knowledge. All the router knows about other areas is that it must send traffic destined to another area to Area 0.
If, as sometimes happens, you have an area that cannot physically attach to Area 0, you must create a virtual link between that area and Area 0. Area 0 must also be contiguous, you cannot have two different Area 0s. You will need to implement a virtual link if Area 0 is split.
If you want redundant connections, then you need to have multiple connections from each area into Area 0.
The reason you cannot use a mesh with OSPF is found in RFC 2328, OSPF Version 2:
3.1. The backbone of the Autonomous System
The OSPF backbone is the special OSPF Area 0 (often written as Area
0.0.0.0, since OSPF Area ID's are typically formatted as IP addresses). The OSPF backbone always contains all area border routers.
The backbone is responsible for distributing routing information
between non-backbone areas. The backbone must be contiguous. However,
it need not be physically contiguous; backbone connectivity can be
established/maintained through the configuration of virtual links.
Virtual links can be configured between any two backbone routers that
have an interface to a common non-backbone area. Virtual links belong
to the backbone. The protocol treats two routers joined by a virtual
link as if they were connected by an unnumbered point-to-point
backbone network. On the graph of the backbone, two such routers are
joined by arcs whose costs are the intra-area distances between the
two routers. The routing protocol traffic that flows along the
virtual link uses intra- area routing only.
3.2. Inter-area routing
When routing a packet between two non-backbone areas the backbone is
used. The path that the packet will travel can be broken up into
three contiguous pieces: an intra-area path from the source to an area
border router, a backbone path between the source and destination
areas, and then another intra-area path to the destination. The
algorithm finds the set of such paths that have the smallest cost.
Looking at this another way, inter-area routing can be pictured as
forcing a star configuration on the Autonomous System, with the
backbone as hub and each of the non-backbone areas as spokes.
The topology of the backbone dictates the backbone paths used between
areas. The topology of the backbone can be enhanced by adding virtual
links. This gives the system administrator some control over the
routes taken by inter-area traffic.
The correct area border router to use as the packet exits the source
area is chosen in exactly the same way routers advertising external
routes are chosen. Each area border router in an area summarizes for
the area its cost to all networks external to the area. After the SPF
tree is calculated for the area, routes to all inter-area destinations
are calculated by examining the summaries of the area border routers.
