Publicación: A POSTERIORI ERROR ANALYSIS OF AN AUGMENTED MIXED-PRIMAL FORMULATION FOR THE STATIONARY BOUSSINESQ MODEL
Fecha
2017
Título de la revista
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Editor
CALCOLO
Resumen
IN AN EARLIER WORK OF US, A NEW MIXED FINITE ELEMENT SCHEME WAS DEVELOPED FOR THE BOUSSINESQ MODEL DESCRIBING NATURAL CONVECTION. OUR METHODOLOGY CONSISTED OF A FIXED-POINT STRATEGY FOR THE VARIATIONAL PROBLEM THAT RESULTED AFTER INTRODUCING A MODIFIED PSEUDOSTRESS TENSOR AND THE NORMAL COMPONENT OF THE TEMPERATURE GRADIENT AS AUXILIARY UNKNOWNS IN THE CORRESPONDING NAVIER-STOKES AND ADVECTION-DIFFUSION EQUATIONS DEFINING THE MODEL, RESPECTIVELY, ALONG WITH THE INCORPORATION OF PARAMETERIZED REDUNDANT GALERKIN TERMS. THE WELL-POSEDNESS OF BOTH THE CONTINUOUS AND DISCRETE SETTINGS, THE CONVERGENCE OF THE ASSOCIATED GALERKIN SCHEME, AS WELL AS A PRIORI ERROR ESTIMATES OF OPTIMAL ORDER WERE STATED THERE. IN THIS WORK WE COMPLEMENT THE NUMERICAL ANALYSIS OF OUR AFOREMENTIONED AUGMENTED MIXED-PRIMAL METHOD BY CARRYING OUT A CORRESPONDING A POSTERIORI ERROR ESTIMATION IN TWO AND THREE DIMENSIONS. STANDARD ARGUMENTS RELYING ON DUALITY TECHNIQUES, AND SUITABLE HELMHOLTZ DECOMPOSITIONS ARE USED TO DERIVE A GLOBAL ERROR INDICATOR AND TO SHOW ITS RELIABILITY. A GLOBALLY EFFICIENCY PROPERTY WITH RESPECT TO THE NATURAL NORM IS FURTHER PROVED VIA USUAL LOCALIZATION TECHNIQUES OF BUBBLE FUNCTIONS. FINALLY, AN ADAPTIVE ALGORITHM BASED ON A RELIABLE, FULLY LOCAL AND COMPUTABLE A POSTERIORI ERROR ESTIMATOR INDUCED BY THE AFOREMENTIONED ONE IS PROPOSED, AND ITS PERFORMANCE AND EFFECTIVENESS ARE ILLUSTRATED THROUGH A FEW NUMERICAL EXAMPLES IN TWO DIMENSIONS.
