Publicación: ERROR ESTIMATES FOR FEM DISCRETIZATIONS OF THE NAVIER-STOKES EQUATIONS WITH DIRAC MEASURES
Fecha
2021
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JOURNAL OF SCIENTIFIC COMPUTING
Resumen
WE ANALYZE, ON TWO DIMENSIONAL POLYGONAL DOMAINS, CLASSICAL LOW?ORDER INF-SUP STABLE FINITE ELEMENT APPROXIMATIONS OF THE STATIONARY NAVIER?STOKES EQUATIONS WITH SINGULAR SOURCES. WE OPERATE UNDER THE ASSUMPTIONS THAT THE CONTINUOUS AND DISCRETE SOLUTIONS ARE SUFFICIENTLY SMALL. WE PERFORM AN A PRIORI ERROR ANALYSIS ON CONVEX DOMAINS. ON LIPSCHITZ, BUT NOT NECESSARILY CONVEX, POLYGONAL DOMAINS, WE DESIGN AN A POSTERIORI ERROR ESTIMATOR AND PROVE ITS GLOBAL RELIABILITY. WE ALSO EXPLORE EFFICIENCY ESTIMATES. WE ILLUSTRATE THE THEORY WITH NUMERICAL TESTS.
