On second-order finite volume approximations for 3D mixed boundary value problems
Copyright policy )On second-order finite volume approximations for 3D mixed boundary value problems
A three-dimensional mixed boundary value problem for the diffusion equation with piecewise constant coefficients is considered. The region under consideration has a simple form and its partition into nonuniform boxes (volumes) is used. Following the known results for two-dimensional problems, the authors construct second-order approximations with error estimates in the maximum and grid-dependent weighted Euclidean norms. Numerical experiments are described for two simple model problems connected with the Poisson equation in the unit square and cube.
numerical examples, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, mixed boundary value problem, diffusion equation, Heat equation, balance matrix, finite volume approximation, finite volume method, difference scheme, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Poisson equation, nonuniform grid, Boundary value problems for second-order elliptic equations, error estimates, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, numerical experiments
numerical examples, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Error bounds for boundary value problems involving PDEs, mixed boundary value problem, diffusion equation, Heat equation, balance matrix, finite volume approximation, finite volume method, difference scheme, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, Poisson equation, nonuniform grid, Boundary value problems for second-order elliptic equations, error estimates, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, numerical experiments
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