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Despite its numerical challenges, finite element method is used to computeviscous fluid flow. A consensus on the cause of numerical problems has beenreached; however, general algorithms---allowing a robust and accuratesimulation for any process---are still missing. Either a very highcomputational cost is necessary for a direct numerical solution (DNS) or somelimiting procedure is used by adding artificial dissipation to the system.These stabilization methods are useful; however, they are often appliedrelative to the element size such that a local monotonous convergence ischallenging to acquire. We need a computational strategy for solving viscousfluid flow using solely the balance equations. In this work, we present ageneral procedure solving fluid mechanics problems without use of anystabilization or splitting schemes. Hence, its generalization to multiphysicsapplications is straightforward. We discuss emerging numerical problems andpresent the methodology rigorously. Implementation is achieved by usingopen-source packages and the accuracy as well as the robustness is demonstratedby comparing results to the closed-form solutions and also by solvingwell-known benchmarking problems.

An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid