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The objective of this article is to discuss the existence and the uniqueness of a weighted extended B-spline- (WEB-spline-) based discrete solution for the 2D Navier-Lame equation of linear elasticity with a different type of mixed boundary condition called boundary condition. Along with the usual weak mixed formulation, we give existence and uniqueness results for weak solution. Then, we illustrate the performance of Ritz–Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects. The numerical tests confirm that, due to the new integration routines, the weighted B-spline solvers have become considerably more efficient.

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WEB-Spline Finite Elements for the Approximation of Navier-Lamé System with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>A</mml:mi><mml:mo>,</mml:mo><mml:mi>B</mml:mi></mml:mrow></mml:msub></mml:math> Boundary Condition

WEB-Spline Finite Elements for the Approximation of Navier-Lamé System with CA,B Boundary Condition