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La méthode des éléments diffus. (The diffuse elements method). (French) Zbl 0725.73085
Summary: A new method is displayed for building sampled-field approximations called “diffuse approximations”. This method provides approximations of the field itself together with its successive derivatives. It preserves the local character of the finite elements required for getting sparse stiffness matrices. Indeed the diffuse approximations may be used for solving partial differential equations, leading to the so called “diffuse elements method”. Its main advantages are: no meshing requirements, regularity of fields, and possibility of direct collocation methods due to this regularity.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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