Publicación: A VIRTUAL ELEMENT DISCRETIZATION FOR THE TIME DEPENDENT NAVIER-STOKES EQUATIONS IN STREAM-FUNCTION FORMULATION
Fecha
2021
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ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS
Resumen
IN THIS WORK, A NEW VIRTUAL ELEMENT METHOD (VEM) OF ARBITRARY ORDER K>=2, FOR THE TIME DEPENDENT NAVIER-STOKES EQUATIONS IN STREAM FUNCTION FORM IS PROPOSED AND ANALYSED. USING SUITABLE PROJECTION OPERATORS, THE BILINEAR AND TRILINEAR TERMS ARE DISCRETISED BY ONLY USING THE PROPOSED DEGREES OF FREEDOM ASSOCIATED WITH THE VIRTUAL SPACE. UNDER CERTAIN ASSUMPTIONS ON THE COMPUTATIONAL DOMAIN, ERROR ESTIMATIONS ARE DERIVED AND SHOWN THAT THE METHOD OPTIMALLY CONVERGENT IN BOTH SPACE AND TIME VARIABLES. FINALLY, TO JUSTIFY THE THEORETICAL ANALYSIS, FOUR BENCHMARK EXAMPLES ARE EXAMINED NUMERICALLY.
