Nonlinear versions of flexurally superconvergent elements
Computer Methods in Applied Mechanics and Engineering
Mixed finite element methods—reduced and selective integration techniques: a unification of concepts
Computer Methods in Applied Mechanics and Engineering - Special edition on the 20th Anniversary
Error analysis of some Galerkin least squares methods for the elasticity equations
SIAM Journal on Numerical Analysis
Error estimates for interpolation by compactly supported radial basis functions of minimal degree
Journal of Approximation Theory
Solving partial differential equations by collocation using radial basis functions
Applied Mathematics and Computation
Meshless Galerkin methods using radial basis functions
Mathematics of Computation
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
Radial basis collocation methods for elliptic boundary value problems
Computers & Mathematics with Applications
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A weighted strong form collocation framework with mixed radial basis approximations for the pressure and displacement fields is proposed for incompressible and nearly incompressible linear elasticity. It is shown that with the proper choice of independent source points and collocation points for the radial basis approximations in the pressure and displacement fields, together with the analytically derived weights associated with the incompressibility constraint and boundary condition collocation equations, optimal convergence can be achieved. The optimal weights associated with the collocation equations are derived based on achieving balanced errors resulting from domain, boundaries, and constraint equations. Since in the proposed method the overdetermined system of the collocation equations is solved by a least squares method, independent pressure and displacement approximations can be selected without suffering from instability due to violation of the LBB stability condition. The numerical solutions verify that the solution of the proposed method does not exhibit volumetric locking and pressure oscillation, and that the solution converges exponentially in both L$$_{2}$$2 norm and H$$_{1}$$1 semi-norm, consistent with the error analysis results presented in this paper.