Displaying similar documents to “Extending Babuška-Aziz's theorem to higher-order Lagrange interpolation”

Three ways of interpolation on finite elements

Šolín, Pavel, Segeth, Karel

Similarity:

Interpolation on finite elements usually occurs in a Hilbert space setting, which means that interpolation techniques involving orthogonal projection are an alternative for the traditional Lagrange nodal interpolation schemes. In addition to the Lagrange interpolation, this paper discusses the global orthogonal projection and the projection-based interpolation. These techniques are compared from the point of view of quality, efficiency, sensitivity to input parameters and other aspects....

A priori error estimates for Lagrange interpolation on triangles

Kenta Kobayashi, Takuya Tsuchiya (2015)

Applications of Mathematics

Similarity:

We present the error analysis of Lagrange interpolation on triangles. A new a priori error estimate is derived in which the bound is expressed in terms of the diameter and circumradius of a triangle. No geometric conditions on triangles are imposed in order to get this type of error estimates. To derive the new error estimate, we make use of the two key observations. The first is that squeezing a right isosceles triangle perpendicularly does not reduce the approximation property of Lagrange...

Interpolation with restrictions -- role of the boundary conditions and individual restrictions

Valášek, Jan, Sváček, Petr

Similarity:

The contribution deals with the remeshing procedure between two computational finite element meshes. The remeshing represented by the interpolation of an approximate solution onto a new mesh is needed in many applications like e.g. in aeroacoustics, here we are particularly interested in the numerical flow simulation of a gradual channel collapse connected with a~severe deterioration of the computational mesh quality. Since the classical Lagrangian projection from one mesh to another...