Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework.
Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions.
Some nonstandard finite element estimates with applications to Poisson and Signorini problems.
A weakly over-penalized symmetric interior penalty method.
A weakly over-penalized symmetric interior penalty method for the biharmonic problem.
Multigrid methods for parameter dependent problems
Finite element approximations of the three dimensional Monge-Ampère equation
In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.
Finite element approximations of the three dimensional Monge-Ampère equation
In this paper, we construct and analyze finite element methods for the three dimensional Monge-Ampère equation. We derive methods using the Lagrange finite element space such that the resulting discrete linearizations are symmetric and stable. With this in hand, we then prove the well-posedness of the method, as well as derive quasi-optimal error estimates. We also present some numerical experiments that back up the theoretical findings.
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