Publicación: MIXED METHODS FOR A STREAM-FUNCTION - VORTICITY FORMULATION OF THE AXISYMMETRIC BRINKMAN EQUATIONS
Fecha
2017
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Editor
JOURNAL OF SCIENTIFIC COMPUTING
Resumen
THIS PAPER IS DEVOTED TO THE NUMERICAL ANALYSIS OF A FAMILY OF FINITE ELEMENT APPROXIMATIONS FOR THE AXISYMMETRIC, MERIDIAN BRINKMAN EQUATIONS WRITTEN IN TERMS OF THE STREAM-FUNCTION AND VORTICITY. A MIXED FORMULATION IS INTRODUCED INVOLVING APPROPRIATE WEIGHTED SOBOLEV SPACES, WHERE WELL-POSEDNESS IS DERIVED BY MEANS OF THE BABU?KA?BREZZI THEORY. WE INTRODUCE A SUITABLE GALERKIN DISCRETIZATION BASED ON CONTINUOUS PIECEWISE POLYNOMIALS OF DEGREE K?1 FOR ALL THE UNKNOWNS, WHERE ITS SOLVABILITY IS ESTABLISHED USING THE SAME FRAMEWORK AS THE CONTINUOUS PROBLEM. OPTIMAL A PRIORI ERROR ESTIMATES ARE DERIVED, WHICH ARE ROBUST WITH RESPECT TO THE FLUID VISCOSITY, AND VALID ALSO IN THE PURE DARCY LIMIT. A FEW NUMERICAL EXAMPLES ARE PRESENTED TO ILLUSTRATE THE CONVERGENCE AND PERFORMANCE OF THE PROPOSED SCHEMES.
