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Discrete Scheme (discrete + scheme)
Selected AbstractsError estimates of CFVE method for fully nonlinear convection-dominated diffusion problemsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2010Yang Zhang Abstract Finite volume method and characteristics finite element method are two important methods for solving the partial differential equations. These two methods are combined in this paper to establish a fully discrete characteristics finite volume method for fully nonlinear convection-dominated diffusion problems. Through detailed theoretical analysis, optimal order H1 norm error estimates are obtained for this fully discrete scheme. Copyright © 2010 John Wiley & Sons, Ltd. [source] On the maximum principle and its application to diffusion equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2007T. Stys Abstract In this article, an analog of the maximum principle has been established for an ordinary differential operator associated with a semi-discrete approximation of parabolic equations. In applications, the maximum principle is used to prove O(h2) and O(h4) uniform convergence of the method of lines for the diffusion Equation (1). The system of ordinary differential equations obtained by the method of lines is solved by an implicit predictor corrector method. The method is tested by examples with the use of the enclosed Mathematica module solveDiffusion. The module solveDiffusion gives the solution by O(h2) uniformly convergent discrete scheme or by O(h4) uniformly convergent discrete scheme. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source] On the numerical approach of the enthalpy method for the Stefan problemNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2004Khaled Omrani Abstract In this article an error bound is derived for a piecewise linear finite element approximation of an enthalpy formulation of the Stefan problem; we have analyzed a semidiscrete Galerkin approximation and completely discrete scheme based on the backward Euler method and a linearized scheme is given and its convergence is also proved. A second-order error estimates are derived for the Crank-Nicolson Galerkin method. In the second part, a new class of finite difference schemes is proposed. Our approach is to introduce a new variable and transform the given equation into an equivalent system of equations. Then, we prove that the difference scheme is second order convergent. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source] On the mixed finite element method with Lagrange multipliersNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003Ivo Babu Abstract In this note we analyze a modified mixed finite element method for second-order elliptic equations in divergence form. As a model we consider the Poisson problem with mixed boundary conditions in a polygonal domain of R2. The Neumann (essential) condition is imposed here in a weak sense, which yields the introduction of a Lagrange multiplier given by the trace of the solution on the corresponding boundary. This approach allows to handle nonhomogeneous Neumann boundary conditions, theoretically and computationally, in an alternative and usually easier way. Then we utilize the classical Babu,ka-Brezzi theory to show that the resulting mixed variational formulation is well posed. In addition, we use Raviart-Thomas spaces to define the associated finite element method and, applying some elliptic regularity results, we prove the stability, unique solvability, and convergence of this discrete scheme, under appropriate assumptions on the mesh sizes. Finally, we provide numerical results illustrating the performance of the algorithm for smooth and singular problems. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 192,210, 2003 [source] | ||||||||||