Interpolation Operators for parabolic Problems

12/08/2022

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We introduce interpolation operators with approximation and stability properties suited for parabolic problems in primal and mixed formulations. We derive localized error estimates for tensor product meshes (occurring in classical time-marching schemes) as well as locally in space-time refined meshes.

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Interpolation Operators for parabolic Problems

Anisotropic Raviart–Thomas interpolation error estimates using a new geometric parameter

General theory of interpolation error estimates on anisotropic meshes, part II

Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes

Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra

On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion

Space-time hp finite elements for heat evolution in laser-based additive manufacturing

Fine stability constants and error bounds for asymmetric approximate saddle point problems

Interpolation Operators for parabolic Problems

Related Research

Anisotropic Raviart–Thomas interpolation error estimates using a new geometric parameter

General theory of interpolation error estimates on anisotropic meshes, part II

Encapsulated generalized summation-by-parts formulations for curvilinear and non-conforming meshes

Efficient Tensor-Product Spectral-Element Operators with the Summation-by-Parts Property on Curved Triangles and Tetrahedra

On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion

Space-time hp finite elements for heat evolution in laser-based additive manufacturing

Fine stability constants and error bounds for asymmetric approximate saddle point problems