A Crank-Nicolson finite volume element method for two-dimensional Sobolev equations
نویسندگان
چکیده
منابع مشابه
A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method
In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than sol...
متن کاملCrank-Nicolson finite element discretizations for a two-dimensional linear Schrödinger-type equation posed in a noncylindrical domain
Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundaryvalue problem for a general Schrödinger-type equation posed on a two space dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain and we approximate its solut...
متن کاملUnconditional convergence of high-order extrapolations of the Crank-Nicolson, finite element method for the Navier-Stokes equations
Error estimates for the Crank-Nicolson in time, finite element in space (CNFE) discretization of the Navier-Stokes equations require a discrete version of the Gronwall inequality, which leads to a time-step restriction. We prove herein that no restriction on the time-step is necessary for a linear, fully implicit variation of CN-FE obtained by extrapolation of the convecting velocity. Previous ...
متن کاملStabilized finite element method based on the Crank-Nicolson extrapolation scheme for the time-dependent Navier-Stokes equations
This paper provides an error analysis for the Crank–Nicolson extrapolation scheme of time discretization applied to the spatially discrete stabilized finite element approximation of the two-dimensional time-dependent Navier–Stokes problem, where the finite element space pair (Xh,Mh) for the approximation (uh, p n h) of the velocity u and the pressure p is constructed by the low-order finite ele...
متن کاملL2-Error Estimates of the Extrapolated Crank-Nicolson Discontinuous Galerkin Approximations for Nonlinear Sobolev Equations
We analyze discontinuous Galerkin methods with penalty terms, namely, symmetric interior penalty Galerkin methods, to solve nonlinear Sobolev equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ∞ L2 error estimates of discontinuous Galerk...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2016
ISSN: 1029-242X
DOI: 10.1186/s13660-016-1131-z