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On residual-based a posteriori error estimation in hp-FEM
TLDR
To do so, the well-known Clément/Scott–Zhang interpolation operator is generalized to the hp-context and new polynomial inverse estimates are presented and an hp-adaptive strategy is proposed.
A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
  • B. Wohlmuth
  • Mathematics, Computer Science
    SIAM J. Numer. Anal.
  • 1 August 2000
TLDR
The original mortar approach to matching at the interface is realized by enforcing an orthogonality relation between the jump and a modified trace space which serves as a space of Lagrange multipliers, which is replaced by a dual space without losing the optimality of the method.
Discretization Methods and Iterative Solvers Based on Domain Decomposition
  • B. Wohlmuth
  • Mathematics, Computer Science
    Lecture Notes in Computational Science and…
  • 27 February 2001
TLDR
This chapter discusses Discretization Techniques Based on Domain Decomposition, which applies to Mortar Finite Element Methods with Alternative Lagrange Multiplier Spaces and Numerical Results.
Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
TLDR
This work describes three possible piecewise multilinear hierarchical interpolation schemes in detail, and documents the features of the sparse grid interpolation software package spinterp for MATLAB.
Residual based a posteriori error estimators for eddy current computation
We consider H (curl ;Ω)-elliptic problems that have been discretized by means of Nedelec's edge elements on tetrahedral meshes. Such problems occur in the numerical computation of eddy currents. From
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
We present and analyze a new a posteriori error estimator for lowest order conforming finite elements. It is based on Raviart--Thomas finite elements and can be obtained locally by a postprocessing
A primal–dual active set strategy for non-linear multibody contact problems
Abstract Non-conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations. For the discretization of a non-linear multibody
A new approach for phase transitions in miscible multi-phase flow in porous media
Abstract The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if
A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method
This paper introduces a new algorithm to define a stable Lagrange multiplier space to impose stiff interface conditions within the context of the extended finite element method. In contrast to
A Reduced Basis Method for Parametrized Variational Inequalities
TLDR
This article proposes a reduced basis variational inequality scheme in a saddle point form and proves existence and uniqueness of the solution, and provides rigorous a posteriori error bounds with a partial offline/online decomposition.
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