Titlebook: Galerkin Finite Element Methods for Parabolic Problems; Vidar Thomée Book 2006Latest edition Springer-Verlag GmbH Germany 2006 Approximati

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Single Step Fully Discrete Schemes for the Inhomogeneous Equation,. Following the approach of Chapter 7 we shall first consider discretization in time of an ordinary differential equation in a Hilbert space setting, and then apply our results to the spatially discrete equation. In view of the work in Chapter 7 for the homogeneous equation with given initial data,

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Multistep Backward Difference Methods,ultistep backward difference quotient of maximum order consistent with the number of time steps involved. We show that when this order is at most 6, then the method is stable and has a smoothing property analogous to that of single step methods of type IV. We shall use these properties to derive bot

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Incomplete Iterative Solution of the Algebraic Systems at the Time Levels,equations has to be solved at each time level of the time stepping procedure, and our analysis has always assumed that these systems are solved exactly. Because in applications these systems are of high dimension, direct methods are most often not appropriate, and iterative methods have to be used.

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The Discontinuous Galerkin Time Stepping Method,es by means of a Galerkin finite element method, which results in a system of ordinary differential equations with respect to time, and then applying a finite difference type time stepping method to this system to define a fully discrete solution. In this chapter, we shall apply the Galerkin method

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A Nonlinear Problem,e restrict our attention to the situation in the beginning of Chapter 1, with a convex plane domain and with piecewise linear approximating functions. We also consider the problem on a finite interval . = (0, . in time; some of the constants in our estimates will depend on ., without explicit mentio

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