Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media
Copyright policy )Convergence Analysis of a Nonconforming Virtual Element Method for Compressible Miscible Displacement Problems in Porous Media
ABSTRACTThis article presents a priori error estimates for the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the conforming virtual element method (VEM) for the approximation of the velocity, while a non‐conforming virtual element approach is employed for the concentration. The pressure is discretized using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. Error estimates are established for velocity, pressure, and concentration. The article also includes numerical results that validate the theoretical estimates.
virtual element methods, Flows in porous media; filtration; seepage, Smoothness and regularity of solutions to PDEs, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, PDEs in connection with fluid mechanics, A priori estimates in context of PDEs, Finite difference methods applied to problems in fluid mechanics, convergence analysis, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, compressible miscible displacement, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, miscible fluid flow, Finite element methods applied to problems in fluid mechanics
virtual element methods, Flows in porous media; filtration; seepage, Smoothness and regularity of solutions to PDEs, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics, PDEs in connection with fluid mechanics, A priori estimates in context of PDEs, Finite difference methods applied to problems in fluid mechanics, convergence analysis, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, compressible miscible displacement, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, miscible fluid flow, Finite element methods applied to problems in fluid mechanics
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