Publicación: A HIGH ORDER MIXED-FEM FOR DIFFUSION PROBLEMS ON CURVER DOMAINS
Fecha
2019
Autores
Título de la revista
ISSN de la revista
Título del volumen
Editor
JOURNAL OF SCIENTIFIC COMPUTING
Resumen
WE PROPOSE AND ANALYZE A HIGH ORDER MIXED FINITE ELEMENT METHOD FOR DIFFUSION PROBLEMS WITH DIRICHLET BOUNDARY CONDITION ON A DOMAIN OMEGA WITH CURVED BOUNDARY GAMMA. THE METHOD IS BASED ON APPROXIMATING OMEGA BY A POLYGONAL SUBDOMAIN D-H, WITH BOUNDARY GAMMA(H), WHERE A HIGH ORDER CONFORMING GALERKIN METHOD IS CONSIDERED TO COMPUTE THE SOLUTION. TO APPROXIMATE THE DIRICHLET DATA ON THE COMPUTATIONAL BOUNDARY GAMMA(H), WE EMPLOY A TRANSFERRING TECHNIQUE BASED ON INTEGRATING THE EXTRAPOLATED DISCRETE GRADIENT ALONG SEGMENTS JOINING GAMMA(H) AND GAMMA. CONSIDERING GENERAL FINITE DIMENSIONAL SUBSPACES WE PROVE THAT THE RESULTING GALERKIN SCHEME, WHICH IS H(DIV; D-H)-CONFORMING, IS WELL-POSED PROVIDED SUITABLE HYPOTHESES ON THE AFOREMENTIONED SUBSPACES AND INTEGRATION SEGMENTS. A FEASIBLE CHOICE OF DISCRETE SPACES IS GIVEN BY RAVIART-THOMAS ELEMENTS OF ORDER K >= 0 FOR THE VECTORIAL VARIABLE AND DISCONTINUOUS POLYNOMIALS OF DEGREE K FOR THE SCALAR VARIABLE, YIELDING OPTIMAL CONVERGENCE IF THE DISTANCE BETWEEN GAMMA(H) AND GAMMA IS AT MOST OF THE ORDER OF THE MESHSIZE H. WE ALSO APPROXIMATE THE SOLUTION IN D-H(C) := OMEGA\(D-H) OVER BAR AND DERIVE THE CORRESPONDING ERROR ESTIMATES. NUMERICAL EXPERIMENTS ILLUSTRATE THE PERFORMANCE OF THE SCHEME AND VALIDATE THE THEORY.
