Mimetic Discretization of Elliptic PDE with Full Tensor Coefficients
نویسندگان
چکیده
This work concentrates upon the Mimetic discretization of elliptic partial differential equations (PDE). Numerical solutions are obtained and discussed for one-dimensional ODE on uniform and irregular grids and two-dimensional PDE on uniform grids. The focal point is to develop a scheme that incorporates the full tensor case on uniform grids in 2-D. The numerical results are then compared to previous well-established methods. Based on its conservative properties and global second order of accuracy, this Mimetic scheme shows higher precision in the tests given, especially on the boundaries.
منابع مشابه
Direct tensor-product solution of one-dimensional elliptic equations with parameter-dependent coefficients
We consider a one-dimensional second-order elliptic equation with a high-dimensional parameter in a hypercube as a parametric domain. Such a problem arises, for example, from the Karhunen Loève expansion of a stochastic PDE posed in a onedimensional physical domain. For the discretization in the parametric domain we use the collocation on a tensor-product grid. The paper is focused on the tenso...
متن کاملConvergence Analysis of the mimetic Finite Difference Method for Elliptic Problems with Staggered Discretizations of Diffusion Coefficients
We propose a family of mimetic discretization schemes for elliptic problems including convection and reaction terms. Our approach is an extension of the mimetic methodology for purely diffusive problems on unstructured polygonal and polyhedral meshes. The a priori error analysis relies on the connection between the mimetic formulation and the lowest order Raviart–Thomas mixed finite element met...
متن کاملA mimetic tensor artificial viscosity method for arbitrary polyhedral meshes
We construct a new mimetic tensor artificial viscosity on general polyhedral meshes. The tensor viscosity is designed as a discretization of the differential operator div (μ∇u) with the full fourth-order tensor μ. We demonstrate performance of the new artificial viscosity on a set of test problems.
متن کاملMimetic Finite Differences for Elliptic Problems
We developed a mimetic finite difference method for solving elliptic equations with tensor coefficients on polyhedral meshes. The first-order convergence estimates in a mesh-dependent H norm are derived. Mathematics Subject Classification. 65N06, 65N12, 65N15, 65N30. Received December 5, 2007. Revised July 21, 2008. Published online December 5, 2008.
متن کاملRecovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data
In this study we consider the recovery of smooth region boundaries of piecewise constant coefficients of an elliptic PDE −∇ · a∇Φ + bΦ = f from data on the exterior boundary ∂Ω. The assumption is that the values of the coefficients (a, b) are known a priori but the information about the geometry of the smooth region boundaries where a and b are discontinous is missing. For the full characterisa...
متن کامل