Mesh Adaptation and Discrete Maximum Principle for 2D Anisotropic Diffusion Problems
نویسندگان
چکیده
Finite element method is widely used to solve diffusion problems. For anisotropic problem, the numerical solution may violate the discrete maximum principle (DMP) even if the triangular mesh satisfies acute type condition. We derive the conditions for a triangular mesh such that the obtained solution satisfies DMP. We also develop the strategy to adapt a given mesh so that the solution is improved.
منابع مشابه
Anisotropic Mesh Adaptation for the Finite Element Solution of Anisotropic Diffusion Problems
Anisotropic diffusion problems arise in many fields of science and engineering and are modeled by partial differential equations (PDEs) or represented in variational formulations. Standard numerical schemes can produce spurious oscillations when they are used to solve those problems. A common approach is to design a proper numerical scheme or a proper mesh such that the numerical solution satis...
متن کاملAnisotropic mesh adaptation for 3D anisotropic diffusion problems with application to fractured reservoir simulation∗
Anisotropic mesh adaptation is studied for linear finite element solution of 3D anisotropic diffusion problems. The M-uniform mesh approach is used, where an anisotropic adaptive mesh is generated as a uniform one in the metric specified by a tensor. In addition to mesh adaptation, preservation of the maximum principle is also studied. Four different metric tensors are investigated: one is the ...
متن کاملAn anisotropic mesh adaptation method for the finite element solution of heterogeneous anisotropic diffusion problems
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numeric...
متن کاملEnforcing non-negativity constraint and maximum principles for diffusion with decay on general computational grids
Abstract. In this paper, we consider anisotropic diffusion with decay, which takes the form α(x)c(x) − div[D(x)grad[c(x)]] = f(x) with decay coefficient α(x) ≥ 0, and diffusivity coefficient D(x) to be a second-order symmetric and positive definite tensor. It is well-known that this particular equation is a second-order elliptic equation, and satisfies a maximum principle under certain regulari...
متن کاملPositive nonlinear CVFE scheme for degenerate anisotropic Keller-Segel system
In this paper, a nonlinear control volume finite element (CVFE) scheme for a degenerate Keller– Segel model with anisotropic and heterogeneous diffusion tensors is proposed and analyzed. In this scheme, degrees of freedom are assigned to vertices of a primal triangular mesh, as in finite element methods. The diffusion term which involves an anisotropic and heterogeneous tensor is discretized on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007