Displaying similar documents to “Error estimates for the semidiscrete finite element approximation of linear nonlocal parabolic equations.”

Galerkin approximations for the linear parabolic equation with the third boundary condition

István Faragó, Sergey Korotov, Pekka Neittaanmäki (2003)

Applications of Mathematics

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We solve a linear parabolic equation in ℝ d , d ≥ 1 , with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the θ -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.

Postprocessing of a finite volume element method for semilinear parabolic problems

Min Yang, Chunjia Bi, Jiangguo Liu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper, we study a postprocessing procedure for improving accuracy of the finite volume element approximations of semilinear parabolic problems. The procedure amounts to solve a source problem on a coarser grid and then solve a linear elliptic problem on a finer grid after the time evolution is finished. We derive error estimates in the and norms for the standard finite volume element scheme and an improved error estimate in the ...

Finite element approximation for degenerate parabolic equations. An application of nonlinear semigroup theory

Akira Mizutani, Norikazu Saito, Takashi Suzuki (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Finite element approximation for degenerate parabolic equations is considered. We propose a semidiscrete scheme provided with order-preserving and L 1 contraction properties, making use of piecewise linear trial functions and the lumping mass technique. Those properties allow us to apply nonlinear semigroup theory, and the wellposedness and stability in L 1 and L ∞ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive L 1 convergence without any convergence...

Lagrangian and moving mesh methods for the convection diffusion equation

Konstantinos Chrysafinos, Noel J. Walkington (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington,   (2006) 2478–2499; Chrysafinos and Walkington,   (2006) 349–366] and the dependence of various constants upon the diffusion parameter is characterized. Error estimates independent...

Superconvergence estimates of finite element methods for American options

Qun Lin, Tang Liu, Shu Hua Zhang (2009)

Applications of Mathematics

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In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and...