Publicación: A FULLY-DISCRETE VIRTUAL ELEMENT METHOD FOR THE NONSTATIONARY BOUSSINESQ EQUATIONS IN STREAM-FUNCTION FORM
Fecha
2023
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COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Resumen
IN THE PRESENT WORK WE PROPOSE AND ANALYZE A FULLY-COUPLED VIRTUAL ELEMENT METHOD OF HIGH ORDER FOR SOLVING THE TWO DIMENSIONAL NONSTATIONARY BOUSSINESQ SYSTEM IN TERMS OF THE STREAM-FUNCTION AND TEMPERATURE FIELDS. THE DISCRETIZATION FOR THE SPATIAL VARIABLES IS BASED ON THE COUPLING C1- AND C0-CONFORMING VIRTUAL ELEMENT APPROACHES, WHILE A BACKWARD EULER SCHEME IS EMPLOYED FOR THE TEMPORAL VARIABLE. WELL-POSEDNESS AND UNCONDITIONAL STABILITY OF THE FULLY-DISCRETE PROBLEM ARE PROVIDED. MOREOVER, ERROR ESTIMATES IN H2- AND H1-NORMS ARE DERIVED FOR THE STREAM-FUNCTION AND TEMPERATURE, RESPECTIVELY. FINALLY, A SET OF BENCHMARK TESTS ARE REPORTED TO CONFIRM THE THEORETICAL ERROR BOUNDS AND ILLUSTRATE THE BEHAVIOR OF THE FULLY-DISCRETE SCHEME.
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Virtual element method, Stream-function, Nonstationary Boussinesq equations, form, Error estimates
