Mixed FEM for Δu = αu

Polak, S. J.

doi:10.1007/978-3-0348-5698-0_18

Cited by 1 publication

(3 citation statements)

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“…Special quadrature rules ensure that the mass matrix has exactly the right properties, and proofs can be given that the coefficient matrix of the system for the unknown potentials and/or carrier concentrations has the M-property. This has been described in detail in [65,67]. A remaining problem is that, in the case of a triangular mesh, the triangles must all be non-obtuse.…”

Section: Non-standard Mixed Finite Element Methodsmentioning

confidence: 99%

“…This has been done in [60] and [61], leading in the latter case to the frequently used Raviart-Thomas elements. Applications to semiconductor device problems started about 1987 in, for example, [15,62,63], with important and necessary improvements developed in [64][65][66][67][68]. Independently, a different type of mixed finite element method using inverse averages was developed in [56,69].…”

Section: Extension To Higher Dimensionsmentioning

confidence: 99%

“…For triangles, the situation is more complicated, and the proof that the resulting coefficient matrix has the M-property is rather involved. The reader is referred to [65,67] for the details of the quadrature rules used in that case, and for proofs of the discrete maximum principle.…”

Section: Practical Considerationsmentioning

confidence: 99%

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Application of finite element methods to the simulation of semiconductor devices

1999

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In this paper a survey is presented of the use of finite element methods for the simulation of the behaviour of semiconductor devices. Both ordinary and mixed finite element methods are considered. We indicate how the various mathematical models of semiconductor device behaviour can be obtained from the Boltzmann transport equation and the appropriate closing relations. The drift-diffusion and hydrodynamic models are discussed in more detail. Some mathematical properties of the resulting nonlinear systems of partial differential equations are identified, and general considerations regarding their numerical approximations are discussed. Ordinary finite element methods of standard and non-standard type are introduced by means of one-dimensional illustrative examples. Both types of finite element method are then extended to two-dimensional problems and some practical issues regarding the corresponding discrete linear systems are discussed. The possibility of using special non-uniform fitted meshes is noted. Mixed finite element methods of standard and non-standard type are described for both one-and two-dimensional problems. The coefficient matrices of the linear systems corresponding to some methods of non-standard type are monotone. Ordinary and mixed finite element methods of both types are applied to the equations of the stationary drift-diffusion model in two dimensions. Some promising directions for future research are described.

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Section: Non-standard Mixed Finite Element Methodsmentioning

confidence: 99%