Concepts inSpacetime meshing with adaptive refinement and coarsening

Spacetime

In physics, spacetime (or space-time, space time, space-time continuum) is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. From a Euclidean space perspective, the universe has three dimensions of space and one dimension of time.
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Ostwald ripening

Ostwald ripening is an observed phenomenon in solid solutions or liquid sols which describes the change of an inhomogeneous structure over time. In other words, over time, small crystals or sol particles dissolve, and redeposit onto larger crystals or sol particles. Dissolution of small crystals or sol particles and the redeposition of the dissolved species on the surfaces of larger crystals or sol particles was first described by Wilhelm Ostwald in 1896.
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Classification of discontinuities

Continuous functions are of utmost importance in mathematics and applications. However, not all functions are continuous. If a function is not continuous at a point in its domain, one says that it has a discontinuity there. The set of all points of discontinuity of a function may be a discrete set, a dense set, or even the entire domain of the function. This article describes the classification of discontinuities in the simplest case of functions of a single real variable taking real values.
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Galerkin method

In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem. In principle, it is the equivalent of applying the method of variation of parameters to a function space, by converting the equation to a weak formulation. Typically one then applies some constraints on the function space to characterize the space with a finite set of basis functions.
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Hyperbolic partial differential equation

In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first n¿1 derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest.
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Polygon mesh

A polygon mesh or unstructured grid is a collection of vertices, edges and faces that defines the shape of a polyhedral object in 3D computer graphics and solid modeling. The faces usually consist of triangles, quadrilaterals or other simple convex polygons, since this simplifies rendering, but may also be composed of more general concave polygons, or polygons with holes. The study of polygon meshes is a large sub-field of computer graphics and geometric modeling.
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Tetrahedron

In geometry, a tetrahedron is a polyhedron composed of four triangular faces, three of which meet at each vertex. It has six edges and four vertices. The tetrahedron is the only convex polyhedron that has four faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point.
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Finite element method

The finite element method (FEM) (its practical application often known as finite element analysis) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations.
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