Most modern methods for solving partial differential equations are based on a variational principle. Probably the most popular variational principle is the Galerkin method, which works extremely well for a wide class of problems. But for some classes of problems, like saddle point problems like the Stokes equations, or first order differential operators, it exhibits some numerical difficulties.
Least Squares finite element methods (LSFEM) provide an alternative way of solving partial differential equations. They recast the original problem into an equivalent minimisation problem, which offers some advantages. Although many problems regarding the LSFEM have been addressed in literature, many question are still open. Some of those questions were addressed in my previous research.
Now the focus of my research shifted to the multiscale modelling of muscle tissue. The aim of my work is to find answers for specific questions regarding muscle cells by utilising novel numerical models. Once these models have been established, they do not only allow virtual experiments which cannot be done in reality but also give a deeper understanding of the underlying molecular mechanisms.