  Cell blebs are protrusions of the cell membrane and can be instrumental for
cell migration. We derive a continuum model for the mechanical and geometrical
aspects of the onset of blebbing in terms of a force balance. It is abstract
and flexible in that it allows for amending force contributions related to
membrane tension or the presence of linker molecules between membrane and cell
cortex. The deforming membrane and all forces are expressed by means of a
parametrisation over a stationary reference surface. A variational formulation
is presented and analysed for well-posedness. For this purpose, we derive a
semi-discrete scheme based on the surface finite element method. We provide a
convergence result and estimates of the error due to the spatial
discretisation. Furthermore, we present a computational framework where
specific models can be implemented and later on conveniently amended if
desired, using a domain specific language implemented in Python. While the high
level program control can be done within the Python scripting environment, the
actual computationally expensive step of evolving the solution over time is
carried out by binding to an efficient software backend. Cell membrane
geometries given in terms of a parametrisation or obtained from image data can
be accounted for. A couple of numerical simulation results illustrate the
approach.
