Tom Hughes made pioneering contributions in many fronts in finite element methods and computational mechanics and has been a prime mover in bringing these fields to a new era. We see all of this in the contributions he made directly, in the contributions he made through the students he trained and associates he guided, and in the contributions made by the friends and colleagues he inspired.

(i) A new Petrov-Galerkin formulation of the Stokes problem is proposed. The new formulation possesses better stability properties than the classical Galerkin/variational method. An error analysis is performed for the case in which both the velocity and pressure are approximated by $C_{0}$ interpolations. Combinations of $C_{0}$ interpolations which are unstable according to the Babuska-Brezzi condition (e.g., equal-order interpolations) are shown to be stable and convergent within the present framework. Calculations exhibiting the good behaviour of the methodology are presented.

(ii) Results of Harten and Tadmor are generalized to the compressible Navier-Stokes equations including heat conduction effects. A symmetric form of the equations is derived in terms of entropy variables. It is shown that finite element methods based upon this form automatically satisfy the second law of thermodynamics and that stability of the discrete solution is thereby guaranteed ab initio.

New finite element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least squares like terms. The additional terms involve integrals over element interiors, and include mesh dependent coefficients. The methods are designed to enhance stability. Consistence is achieved in the sense that exact solutions identically satisfy the variational equations. Applied to several problems, simple finite element interpolations are rendered convergent, including convenient equal order interpolations which are generally unstable within the Galerkin approach. The methods are divided into two classes according to the manner in which stability is attained: (1) Circumventing Babuska-Brezzi condition methods; (2) Satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods.

Leo struggled against a severe liver disease, caused by Wilson's disease, which required a liver transplant he could finally accomplish in 2004, at the University of Colorado Hospital. About this, he wrote on his Facebook page: 'It was a dramatic year. I spent one year waiting for a liver transplant. Towards the end I was having a series of liver failures until I completely passed out. The doctor told my wife I had three days to live, and he was hoping a liver would appear. It did! And all ended well!'

... he joined our team at the High Performance Computing Center at the Alberto Luiz Coimbra Institute for Graduate Studies and Research at the Federal University of Rio de Janeiro, collaborating as a consultant in Research and Development projects for the oil industry. Many fruitful meetings and discussions with Leo around themes such as fluid-structure interaction and its underlying intricacies provided deeper insight into the problem and, by all means, enjoyable moments to be remembered by all team members.

Assessing the impact of existing fractures and faults for reservoir management, in one aspect, may comprise employing a numerical mesh to generate a geomechanical model, the numerical mesh representing a geological reservoir and its surrounding regions, the numerical mesh comprising delimitation associated with regions and layering of geology without constraining the numerical mesh to explicitly represent a fault or fracture, initialising the geomechanical model to define initial stress-strain compatible with measured stress in well locations associated with the geological reservoir, generating a fluid-flow model employing the numerical mesh, solving for a coupled solution of the fluid-flow model and the geomechanical model, and employing the solved fluid-flow model and the geomechanical model to assess the impact.

His experience in mechanical engineering with emphasis in numerical methods allowed him to act, among others, on the following subjects: stabilised methods for fluids, solids and acoustics, residual-free methods, and methods for enhanced transport equations. Leo's publication record includes works on stabilised methods, Galerkin least squares methods, unusual stabilised methods, residual-free bubbles, discontinuous enrichment methods, and Petrov-Galerkin enrichment methods.

Leo was a highly cited author ... and during his brilliant career he had a major impact in the development and analysis of innovative finite element methods. Leo ... was a generous, polite and funny friend who loved good food and travelling. He is survived by his wife Lucia and his two daughters Louise and Lais. He will be dearly missed by his several friends all over the world.