  The problem of a plane strain hydraulic fracture propagating in a layered
formation is considered. Fracture toughness, in-situ stress, and leak-off
coefficient are assumed to vary by layer, while the elastic properties are kept
constant throughout the domain for simplicity. The purpose of this study is to
develop a numerical algorithm based on a fixed mesh approach, which is capable
to solve the above problem accurately using elements which can even be larger
than the layer size. In order to do this, the concept of fictitious tip stress
is first introduced for determining the fracture front location. In this
technique, an additional stress is applied to the tip element with the purpose
to suppress opening and to mimic width corresponding to the actual fracture
front location. A theoretical basis for this concept has been established and
it is further calibrated for piece-wise constant elements. Once the ability to
track the crack front location is developed, the effect of layers is included
by vary properties as a function of front location. Several numerical examples
benchmarking the numerical solution, as well as highlighting capabilities of
the algorithm to tackle multiple thin layers accurately are presented.
