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An improvement of the classical finite element method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with Non-Uniform Rational B-Splines (NURBS). Here, the two-dimensional case is presented. For elements not intersecting the boundary, a standard finite element interpolation and numerical integration is used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NEFEM is at least one order of magnitude more precise than the corresponding isoparametric finite element in every numerical example shown.

This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision NEFEM is also more computational efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing accurate solution with coarse meshes and high order interpolations, makes NEFEM a more efficient strategy than classical isoparametric FE.

Abstract

Background: Jurisprudence is a science whose basis is moral and the word of any legal institution, especially the power of attorney is based on representation and permission of a person is based on morality. It is shown in the history of civilization, history and the evolution of peoples and nations that there have always been people have taken on the task of defending and realizing the right for another and in another name, where the person did not have the help and ability. Therefore, in according to this ethical issue, attorney representation is considered irreplaceable and permissible.

Conclusion: The attorney representation is usually known through two faces, which both of them are based on ethics and its continuity is also based on ethics. Its main face is the "attorney representation" that is the subject of the civil law, whose general rules are defined in terms of definition and conditions of its conclusion and its effects in this law.  The other face is "judicial representation of attorney" which is mainly viewed with the same principles of civil advocacy. Advocacy, as well as close to civil advocacy contains a special nature of independent contractual representation influenced by the help of the people and the defense of the oppressed as a matter of ethics under the guise of observing the interests of the client.

Abstract

Jurisprudence is a science whose basis is moral and the word of any legal institution, especially the power of attorney is based on representation and permission of a person is based on morality. It is shown in the history of civilization, history and the evolution of peoples and nations that there have always been people have taken on the task of defending and realizing the right for another and in another name, where the person did not have the help and ability. Therefore, in according to this ethical issue, attorney representation is considered irreplaceable and permissible. The attorney representation is usually known through two faces, which both of them are based on ethics and its continuity is also based on ethics. Its main face is the "attorney representation" that is the subject of the civil law, whose general rules are defined in terms of definition and conditions of its conclusion and its effects in this law. The other face is "judicial representation of attorney" which is mainly viewed with the same principles of civil advocacy. Advocacy, as well as close to civil advocacy contains a special nature of independent contractual representation influenced by the help of the people and the defense of the oppressed as a matter of ethics under the guise of observing the interests of the client.