Quadratic Finite Volume Element Methods Based on Optimal Stress Points for Solving One-Dimensional Parabolic Problems
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"Quadratic Finite Volume Element Met..." refers background or methods in this paper
...0 ( ) ( , ), ( , ) ( , ) (0, ] ( , ) ( , ) 0, 0, (0, ] ( ,0) ( ), ( , ) u u p f x t x t a b T t dx x u b t u a t t T x u x u x x a b (1)...
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...Then the Crank-Nicolson Fully discrete finite volume element format that Corresponding to problem (1) is request ( 1,2, , ), n h h u U n J such that 1/2 1/2...
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...b t t a a u v pu v dx (3) So the solution of the equations (2) is called generalized solution of the problem(1) let a division mesh h T for [ , ] I a b ,Nodes are 0 1 2 ....
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...t u u u u t x The associated weak formulation of problem (1) is: find 1 ( , ) : ( )(0 ), E u u t U H I t T such that...
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...Theorem 1 set u is the solution of the problem (1) and n h u is the solution of Fully discrete finite volume element format (8), then 1)...
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