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- Trygve K. Nilssen, XUE–CHENG TAI, Ragnar Winther
- 2001

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counter example is given to show that the Morley method diverges for the reduced… (More)

- Trygve K. Nilssen, Xue-Cheng Tai, Ragnar Winther
- Math. Comput.
- 2001

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counterexample is given to show that the Morley method diverges for the reduced… (More)

- Kent-André Mardal, Trygve K. Nilssen, Gunnar Andreas Staff
- SIAM J. Scientific Computing
- 2007

In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank–Nicolson schemes can be reused for higher–order fully implicit Runge–Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order–optimal for A–stable and irreducible Runge–Kutta schemes with invertible… (More)

- Bjørn-Ove Heimsund, Tony F. Chan, Trygve K. Nilssen, Xue-Cheng Tai
- Analysis and Optimization of Differential Systems
- 2002

Recently, the authors introduced a preconditioner for the linear systems that arise from fully implicit Runge-Kutta time stepping schemes applied to parabolic PDEs [9]. The preconditioner was a block Jacobi preconditioner, where each of the blocks were based on standard preconditioners for low-order time discretizations like implicit Euler or… (More)

Gunnar A. Staff and Kent-Andre Mardal and Trygve K. Nilssen ∗ Simula Research Laboratory 1325 Lysaker, Norway e-mail: gunnaran@simula.no web page:http://www.simula.no/portal memberdata/gunnaran † Simula Research Laboratory 1325 Lysaker, Norway e-mail:kent-and@simula.no web page:http://www.simula.no/portal memberdata/kent-and †† Scandpower Petrolium… (More)

Finite element methods for some elliptic fourth order singular perturbation problems are discussed. We show that if such problems are discretized by the nonconforming Morley method, in a regime close to second order elliptic equations, then the error deteriorates. In fact, a counter example is given to show that the Morley method diverges for the reduced… (More)

Numerical identification of diffusion parameters in a nonlinear convection–diffusion equation is studied. This partial differential equation arises as the saturation equation in the fractional flow formulation of the two–phase porous media flow equations. The forward problem is discretized with the finite difference method, and the identification problem is… (More)

- Tom Lyche, Trygve K. Nilssen, Ragnar Winther
- Adv. Comput. Math.
- 2002

Tom Lyche, a Trygve K. Nilssen, b and Ragnar Winther c,∗ a Department of Informatics, University of Oslo, P.O. Box 1080 Blindern, 0316 Oslo, Norway E-mail: tom@ifi.uio.no b Department of Mathematics, University of Bergen, Johannes Brunsgt. 12, 5007 Bergen, Norway E-mail: Trygve.Nilssen@mi.uib.no c Department of Informatics and Department of Mathematics,… (More)

We consider numerical identification of the piecewise constant permeability function in a nonlinear parabolic equation, with the augmented Lagrangian method. By studying this problem, we aim at also gaining some insight into the potential ability of the augmented Lagrangian method to handle permeability estimation within the full two-phase porous-media flow… (More)