In this paper, two nonconforming finite elements are discussed. They pass the generlized patch test and can be used in the numerical solution of second order elliptic problems.
In this paper, two nonconforming finite elements are discussed. They pass the generlized patch test and can be used in the numerical solution of second order elliptic problems.
Stabilized hybrid finite element methods are developed for the second order elliptic problem. These methodologies are characterized by the following properties:[1] any stabilizing parameter is avoided. [2] the uniform...
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Stabilized hybrid finite element methods are developed for the second order elliptic problem. These methodologies are characterized by the following properties:[1] any stabilizing parameter is avoided. [2] the uniform ellipticity is obtained.[3] hybrid element pairs can be depicted as either nonconforming or can be expanded as conforming elements through the method used. [4] optimal error bounds are established.[5] the same arguments as this note may be easily applied to other three dimensional problems.
A new way to calculate the formal energy of symplectic RK’methods is developed. The approach is much easier to manipulate than traditional methods and doesn’t require any differential or integral calculus.
A new way to calculate the formal energy of symplectic RK’methods is developed. The approach is much easier to manipulate than traditional methods and doesn’t require any differential or integral calculus.
Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tra...
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Ray tracing is a basic aspect in tomography. To solve the caustic problem in inhomogeneous media using Maslov asymptotic theory, we need to calculate the position and slowness vector at every point. Therefore, ray tracing must rely on the ray equations in Hamiltonian form. In this paper, fourth order symplectic scheme and nonsymplectic Runge-Kutta scheme are compared in ray tracing for sinusoidal velocity model. The result indicates that ray paths obtained by two schemes are almost the same. But on keeping Hamilton quantities, the symplectic scheme is far better than the Runge-Kutta scheme. On computing travel time for Htamiltonian system with T parameter, we use trapezoid formula for numerical integration. The result coincides with that obtained using Hamiltonian system with t parameter.
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