Peter Hansbo's research is aimed at developing improved (i.e., faster, more accurate, simpler) numerical models for the solution of problems related to classical field theories, i.e., systems of partial differential equations that describe phenomena such as convection, strength of materials, and wave propagation. In particular he focuses on multiphysics problems, e.g., the connection between various physical systems such as fluid-structure interaction.Peter Hansbo is known mainly for his work on adaptive Finite Element Methods (FEM), stabilised FEM for convection dominated flow, discontinuous FEM, and for methods for connecting models via interfaces

• Part I. Elementary mathematical models in continuum mechanics 1. Mathematical modeling with ordinary differential equations 2. Boundary value problems in several dimensions 3. Time dependent problems 4. Mixed problemsPart II. Introduction to numerical modeling 5. The basics 6. Adaptive finite element methods 7. Time-dependent problems 8. Mixed methodsPart III. Advanced and nonlinear models in continuum mechanics 9. Material Models in Small Deformation Solid Mechanics 10. General Principles in Continuum Mechanics 11. Large Deformation Solid Mechanics 12. Thermodynamics 13. Fluids 14. Stability problems 15. Contact problemsPart IV. Advanced numerical modeling 16. Solution algorithms for linear systems of equations 17. Non-linear problems 18. Adaptive finite element methods 19. Practical Adaptivity and Mesh Generation 20. Finite Elements in Fluids 21. Non-conforming finite element methods