Publicación: A POSTERIORI ERROR ANALYSIS OF A MOMENTUM AND THERMAL ENERGY CONSERVATIVE MIXED FEM FOR THE BOUSSINESQ EQUATIONS
Fecha
2022
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CALCOLO
Resumen
IN THIS PAPER WE COMPLEMENT THE STUDY OF A NEW MIXED FNITE ELEMENT SCHEME, ALLOWING CONSERVATION OF MOMENTUM AND THERMAL ENERGY, FOR THE BOUSSINESQ MODEL DESCRIBING NATURAL CONVECTION AND DERIVE A RELIABLE AND EFCIENT RESIDUAL-BASED A POSTERIORI ERROR ESTIMATOR FOR THE CORRESPONDING GALERKIN SCHEME IN TWO AND THREE DIMENSIONS. MORE PRECISELY, BY EXTENDING STANDARD TECHNIQUES COMMONLY USED ON HILBERT SPACES TO THE CASE OF BANACH SPACES, SUCH AS LOCAL ESTIMATES, SUITABLE HELMHOLTZ DECOMPOSITIONS AND THE LOCAL APPROXIMATION PROPERTIES OF THE CLÉMENT AND RAVIART?THOMAS OPERATORS, WE DERIVE THE AFOREMENTIONED A POSTERIORI ERROR ESTIMATOR ON ARBITRARY (CONVEX OR NON-CONVEX) POLYGONAL AND POLYHEDRAL REGIONS. IN TURN, INVERSE INEQUALITIES, THE LOCALIZATION TECHNIQUE BASED ON BUBBLE FUNCTIONS, AND KNOWN RESULTS FROM PREVIOUS WORKS, ARE EMPLOYED TO PROVE THE LOCAL EFCIENCY OF THE PROPOSED A POSTERIORI ERROR ESTIMATOR. FINALLY, TO ILLUSTRATE THE PERFORMANCE OF THE ADAPTIVE ALGORITHM BASED ON THE PROPOSED A POSTERIORI ERROR INDICATOR AND TO CORROBORATE THE THEORETICAL RESULTS, WE PROVIDE SOME NUMERICAL EXAMPLES.
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STATIONARY BOUSSINESQ EQUATIONS, RELIABILITY, RAVIART?THOMAS ELEMENTS, MIXED FNITE ELEMENT METHOD, LOCAL EFCIENCY, CONSERVATION OF THERMAL ENERGY, CONSERVATION OF MOMENTUM, BANACH SPACES, A POSTERIORI ERROR ESTIMATOR
