Publicación: A C1 VIRTUAL ELEMENT METHOD FOR THE STATIONARY QUASI-GEOSTROPHIC EQUATIONS OF THE OCEAN
Fecha
2022
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COMPUTERS & MATHEMATICS WITH APPLICATIONS
Resumen
IN THIS PRESENT PAPER, WE PROPOSE AND ANALYZE A -CONFORMING VIRTUAL ELEMENT METHOD TO SOLVE THE SO-CALLED ONE-LAYER STATIONARY QUASI-GEOSTROPHIC EQUATIONS (QGE) WITH APPLICATIONS IN THE LARGE SCALE WIND-DRIVEN OCEAN CIRCULATION, FORMULATED IN TERMS OF THE STREAM-FUNCTION. THIS PROBLEM CORRESPONDS TO A NONLINEAR FOURTH ORDER PARTIAL DIFFERENTIAL EQUATION. THE VIRTUAL SPACE AND THE DISCRETE SCHEME ARE BUILT IN A STRAIGHTFORWARD WAY DUE TO THE FLEXIBILITY OF THE VIRTUAL APPROACH. UNDER THE ASSUMPTION OF SMALL DATA, WE PROVE WELL-POSEDNESS OF THE DISCRETE PROBLEM BY USING A FIXED-POINT STRATEGY AND UNDER STANDARD ASSUMPTIONS ON THE COMPUTATIONAL DOMAIN, WE ESTABLISH ERROR ESTIMATES IN -NORM FOR THE STREAM-FUNCTION. FINALLY, WE REPORT FOUR NUMERICAL EXPERIMENTS THAT ILLUSTRATE THE BEHAVIOR OF THE PROPOSED SCHEME AND CONFIRM OUR THEORETICAL RESULTS ON DIFFERENT FAMILIES OF POLYGONAL MESHES.
