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

István Faragó; Sergey Korotov; Pekka Neittaanmäki

Displaying similar documents to “Galerkin approximations for the linear parabolic equation with the third boundary condition”

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 $L^{\infty}$ , respectively, of the scheme are established. Under certain hypotheses on the data, we also derive $L^{1}$ convergence without any convergence...

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

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We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in $d$ space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order $k + 1$ in the $L_{2}$ -norm if the method uses polynomials of order $k$ . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order $k + 1$ . Further we consider a residual-based...

Finite element analysis for unilateral problems with obstacles on the boundary

Jaroslav Haslinger (1977)

Aplikace matematiky

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Finite element analysis of unilateral problems with obstacles on the boundary is given. Provided the exact solution is smooth enough, we obtain the rate of convergence $0 (h)$ for the case of one and two (lower and upper) obstacles on the boundary. At the end of this paper the proof of convergence without any regularity assumptions on the exact solution $u$ is given.

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise, Sarah Cochez-Dhondt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into . We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete...

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...