Abstract
A hybrid finite element scheme, based on assumed deviatoric fluid stresses in the element and continuous velocity fields at the element-boundaries, is presented. The deviatoric stress and hydrostatic pressure field are subject a priori to the constraints of balance of momenta, the advantages of the present scheme are discussed, and its versatility is demonstrated through a few numerical examples. Studies of convergence and stability of the method are included in Part II of the paper.
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