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Mass conservation of finite element methods for coupled flow
Mass conservation of finite element methods for coupled flow

... make the fundamental decision of choosing either a continuous or discontinuous pressure approximation. Due to (17), the incompressibility constraint ∇ · u = 0 from (1) is fulfilled only in an approximate sense. If discontinuous pressure approximations are used, the mass conservation is satisfied mor ...
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Development of Advanced Simulation Methods for Solid Earth

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Форма 502
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... the same node is equal to: y( xn ,i )  y nr̂ ,i  O( h k 3 ); i  1, k̂ . From these relations it follows that the estimation of truncation error formula of lower order accuracy, k-point method, can be approximately calculated as follows: ynr ,i  ynr̂ ,i ;i  1,k . This approach to evaluating the ...
Flux-based level set method on rectangular grids and computation
Flux-based level set method on rectangular grids and computation

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Rate of Convergence of Basis Expansions in Quantum Chemistry

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CSci 136: Lab 2 Exercise

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Finding Multiple Roots of Nonlinear Algebraic Equations Using S

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IOSR Journal of Mathematics (IOSR-JM)
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Tunneling in Double Barriers

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COMBINED MEASUREMENT OF FLOW VELOCITY AND FILLING WITHIN

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... Figure 5 Effect of step size in Euler’s method. Can one solve a definite integral using numerical methods such as Euler’s method of solving ordinary differential equations? Let us suppose you want to find the integral of a function f (x) b ...
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Root-finding algorithm

A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f(x) = 0, for a given function f. Such an x is called a root of the function f.This article is concerned with finding scalar, real or complex roots, approximated as floating point numbers. Finding integer roots or exact algebraic roots are separate problems, whose algorithms have little in common with those discussed here. (See: Diophantine equation for integer roots)Finding a root of f(x) − g(x) = 0 is the same as solving the equation f(x) = g(x). Here, x is called the unknown in the equation. Conversely, any equation can take the canonical form f(x) = 0, so equation solving is the same thing as computing (or finding) a root of a function.Numerical root-finding methods use iteration, producing a sequence of numbers that hopefully converge towards a limit, which is a root. The first values of this series are initial guesses. Many methods computes subsequent values by evaluating an auxiliary function on the preceding values. The limit is thus a fixed point of the auxiliary function, which is chosen for having the roots of the original equation as fixed points.The behaviour of root-finding algorithms is studied in numerical analysis. Algorithms perform best when they take advantage of known characteristics of the given function. Thus an algorithm to find isolated real roots of a low-degree polynomial in one variable may bear little resemblance to an algorithm for complex roots of a ""black-box"" function which is not even known to be differentiable. Questions include ability to separate close roots, robustness against failures of continuity and differentiability, reliability despite inevitable numerical errors, and rate of convergence.
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