Simple Co approximations for the computation of incompressible flows
Computer Methods in Applied Mechanics and Engineering
SIAM Journal on Numerical Analysis
Stabilization of Low-order Mixed Finite Elements for the Stokes Equations
SIAM Journal on Numerical Analysis
Stabilized Finite Element Methods Based on Multiscale Enrichment for the Stokes Problem
SIAM Journal on Numerical Analysis
A Symmetric Nodal Conservative Finite Element Method for the Darcy Equation
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Computers & Mathematics with Applications
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This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. The initial unstable $\mathbb{P}_1\times\mathbb{P}_l$, $l=0,1$, finite element space is enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unchanged while giving rise to new stable and consistent methods for continuous and discontinuous approximation spaces for the pressure. The resulting methods do not need the use of a macroelement grid structure and are parameter-free. The numerical analysis is carried out showing optimal convergence in natural norms, and moreover, two ways of rendering the velocity field locally mass conservative are proposed. Some numerics validate the theoretical results.