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Introduction to the web-method and its applications. (English) Zbl 1070.65118
The proposed finite element method is based on a tensor product grid, hence no mesh generation is needed. On this grid B-splines are introduced and modified using a positive weight function. Using this weight function boundary conditions are implemented, hence there is no need to start with boundary conforming elements. Suggestions on how to construct such a weight function are given, the treatment of splines with part of their support outside of the computational domain is also discussed. Optimal order of approximation is shown under an assumption of smoothness on the solution and the weight function. The behavior of the method is demonstrated on three applications (Laplace equation, linear elasticity, thin plate model).

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
41A15 Spline approximation
74S05 Finite element methods applied to problems in solid mechanics
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
74B05 Classical linear elasticity
74K20 Plates
35J25 Boundary value problems for second-order elliptic equations
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