Publicación: A MORLEY-TYPE VIRTUAL ELEMENT APPROXIMATION FOR A WIND-DRIVEN OCEAN CIRCULATION MODEL ON POLYGONAL MESHES
Fecha
2023
Título de la revista
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Editor
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Resumen
IN THIS WORK, WE PROPOSE AND ANALYZE A MORLEY-TYPE VIRTUAL ELEMENT METHOD TO APPROXIMATE THE STOMMEL?MUNK MODEL IN STREAM-FUNCTION FORM. THE DISCRETIZATION IS BASED ON
THE FULLY NONCONFORMING VIRTUAL ELEMENT APPROACH PRESENTED IN ANTONIETTI ET AL., (2018) AND ZHAO ET AL., (2018). THE ANALYSIS RESTRICTS TO SIMPLY CONNECTED POLYGONAL DOMAINS,
NOT NECESSARILY CONVEX. UNDER STANDARD ASSUMPTIONS ON THE COMPUTATIONAL DOMAIN WE
DERIVE SOME INVERSE ESTIMATES, NORM EQUIVALENCE AND APPROXIMATION PROPERTIES FOR AN
ENRICHING OPERATOR EH DEFINED FROM THE NONCONFORMING SPACE INTO ITS H2-CONFORMING COUNTERPART. WITH THE HELP OF THESE TOOLS WE PROVE OPTIMAL ERROR ESTIMATES FOR THE
STREAM-FUNCTION IN BROKEN H2-, H1- AND L2-NORMS UNDER MINIMAL REGULARITY CONDITION ON THE WEAK SOLUTION. EMPLOYING POSTPROCESSING FORMULAS AND ADEQUATE POLYNOMIAL
PROJECTIONS WE COMPUTE FROM THE DISCRETE STREAM-FUNCTION FURTHER FIELDS OF INTEREST, SUCH AS: THE VELOCITY AND VORTICITY. MOREOVER, FOR THESE POSTPROCESSED VARIABLES WE ESTABLISH
ERROR ESTIMATES. FINALLY, WE REPORT PRACTICAL NUMERICAL EXPERIMENTS ON DIFFERENT FAMILIES OF POLYGONAL MESHES.
Descripción
Palabras clave
Velocity?vorticity recovery, Stream-function, Polygonal meshes, Ocean circulation model, Nonconforming virtual element, Error estimates
