We solved eight examples, where we got numerical solutions that are equal to the exact ones if the two unknown functions and the four given kernels are algebraic functions. The solutions that we obtained converge strongly with the exact solutions in the case that the data function is a ...
norm are proved in case of both, a first-order backward euler method and a second-order two-step method in time. these results are based on new estimates of the time dependent interpolation operator derived in this work. preservation of the total mass is verified for both choices of the ...
easy mathematical formula for square, cube with solved examples algebra square root a+b Geometry (McDougal Littell) and a calculator find and simplify the difference quotient calculator algebraic power problems printable worksheets showing distributive property year 7 square root and cube root ...
Two interpolations are tested in numerical examples; one with a single node per element which results in a constant interpolation and one with two nodes per element, resulting in a C0 continuous interpolation across the subdomains. The contact integration domain discretisation follows the non-mortar ...
Often trilinear (or higher-order) interpolation is used when sending fluid variables to the particle location. Special care needs to be taken to estimate the undisturbed fluid quantities in the vicinity of the particle. This was the topic of Chapter 8. Here, we focus on the back-coupling of...
An interpolation method based on B-splines functions combined with a new collocation method is presented. Finally, for showing efficiency of the method we give some numerical examples.doi:10.1016/j.amc.2007.02.031K. MaleknejadH. DeriliAPPLIED MATHEMATICS AND COMPUTATION -ELSEVIER-...
Two examples are solved. It turns out that the interpolate solutions are obtained equal to the exact solutions for analytic given functions and strongly close to the exact ones for non-analytic functions, which confirms the precision and superiority of the proposed method.Shoukralla, E. S....
Here, one mortar primitive has to be determined and continuity is either enforced using interpolation for intersecting nodes, or with a weak equality condition for intersecting edges. The third approach, consists of explicitly defining the entire surface mesh for which the discrete Lagrange multiplier ...
We solved five examples, two for non-singular equations and three for weakly singular equations. By adopting lower interpolation degrees, the interpolated solutions for non-singular equations are shown to be equal to the exact ones, whereas, for singular equations, they are found to strongly ...
An ‘empirical interpolation’ method: Application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Math. 2004, 339, 667–672. [Google Scholar] [CrossRef] Chaturantabut, S.; Sorensen, D.C. Nonlinear Model Reduction via Discrete Empirical Interpolation. SIAM...