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39 relations: Affine transformation, Bilinear form, Boundary value problem, Bounded operator, Cauchy–Schwarz inequality, Coercive function, Complex number, Continuous function, Doctor of Philosophy, Elliptic operator, Elliptic partial differential equation, Energetic space, Energy, Finite element method, Force density, Gravity, Hilbert space, Inner product space, Integration by parts, Jean Céa, Lemma (mathematics), Lp space, Mathematics, Norm (mathematics), Partial differential equation, Partition of an interval, Piecewise linear function, Polynomial, Projection (linear algebra), Real number, Rope, Sesquilinear form, Sobolev space, Square-integrable function, Taylor's theorem, Unit vector, Up to, Weak derivative, Weak formulation.
Affine transformation
In geometry, an affine transformation, affine mapBerger, Marcel (1987), p. 38.
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Bilinear form
In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.
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Boundary value problem
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions.
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Bounded operator
In functional analysis, a bounded linear operator is a linear transformation L between normed vector spaces X and Y for which the ratio of the norm of L(v) to that of v is bounded above by the same number, over all non-zero vectors v in X. In other words, there exists some M\ge 0 such that for all v in X The smallest such M is called the operator norm \|L\|_ \, of L. A bounded linear operator is generally not a bounded function; the latter would require that the norm of L(v) be bounded for all v, which is not possible unless L(v).
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Cauchy–Schwarz inequality
In mathematics, the Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas.
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Coercive function
In mathematics, a coercive function is a function that "grows rapidly" at the extremes of the space on which it is defined.
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Complex number
A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.
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Continuous function
In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.
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Doctor of Philosophy
A Doctor of Philosophy (PhD or Ph.D.; Latin Philosophiae doctor) is the highest academic degree awarded by universities in most countries.
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Elliptic operator
In the theory of partial differential equations, elliptic operators are differential operators that generalize the Laplace operator.
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Elliptic partial differential equation
Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic.
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Energetic space
In mathematics, more precisely in functional analysis, an energetic space is, intuitively, a subspace of a given real Hilbert space equipped with a new "energetic" inner product.
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Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
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Finite element method
The finite element method (FEM), is a numerical method for solving problems of engineering and mathematical physics.
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Force density
In fluid mechanics, the force density is the negative gradient of pressure.
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Gravity
Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.
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Hilbert space
The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space.
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Inner product space
In linear algebra, an inner product space is a vector space with an additional structure called an inner product.
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Integration by parts
In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative.
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Jean Céa
Jean Céa (born 1932, Aïn Témouchent) is a French mathematician.
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Lemma (mathematics)
In mathematics, a "helping theorem" or lemma (plural lemmas or lemmata) is a proven proposition which is used as a stepping stone to a larger result rather than as a statement of interest by itself.
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Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the ''p''-norm for finite-dimensional vector spaces.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Norm (mathematics)
In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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Partition of an interval
In mathematics, a partition of an interval on the real line is a finite sequence of real numbers such that In other terms, a partition of a compact interval is a strictly increasing sequence of numbers (belonging to the interval itself) starting from the initial point of and arriving at the final point of.
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Piecewise linear function
In mathematics, a piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.
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Real number
In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.
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Rope
A rope is a group of yarns, plies, fibers or strands that are twisted or braided together into a larger and stronger form.
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Sesquilinear form
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.
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Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of ''Lp''-norms of the function itself and its derivatives up to a given order.
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Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.
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Taylor's theorem
In calculus, Taylor's theorem gives an approximation of a k-times differentiable function around a given point by a k-th order Taylor polynomial.
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Unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.
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Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
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Weak derivative
In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L''p'' space \mathrm^1().
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Weak formulation
Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations.
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Cea lemma, Cea's lemma, Céa lemma.
References
[1] https://en.wikipedia.org/wiki/Céa's_lemma
