This is the limiting drift rate for the process that now depends on the spatial variable for a spatially inhomogeneous process.
The spatial variable \(x\) is fixed here.
We now semi-discretise problem (48) in the spatial variable.
The polynomial chaos (PC) expansion modes are shown to be smooth functions of the spatial variable x, although each solution realization is discontinuous in the spatial variable x.
The regularity in the spatial variable can then be converted into regularity in time.
Rothe's method for time discretization and Crouseix-Raviart nonconforming finite element method to the spatial variable.
In [6], the authors used the simplified Tikhonov method to identify the spatial variable heat source.
For approximating the spatial variable, a new approach which is introduced by Bozzini et al.
The curvature is taken as an arbitrary function of the spatial variable.
The spatial variable is transformed into an independent variable that satisfies the boundary conditions.
The introduction of spatial variable experimental design offers a convenient tool to help solving this problem.
