The development of numerical methods for the solution of complex problems in engineering and science, mostly at the continuum scale. Complex rheology: multiscale and continuum methods for incompressible viscoelastic flows. Multiphase flows: compressible and incompressible flows of fluids and elastic-plastic solids in time-dependent domains, interfacial processes. Constitutive modeling: equations of state, thermodynamic modeling, symmetry invariants. Charged systems: plasma physics, boundary charge and bilayer problems.