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- Bernardo Cockburn, Johnny Guzman, Haiying Wang, Long Chen, Michael Holst, Jinchao Xu +18 others
- 2010

1 Superconvergent discontinuous Galerkin methods for second-order elliptic problems / A multiscale finite element method for partial differential equations posed in domains with rough boundaries / Alexandre L. Madureira 35 Convergence and optimality of adaptive mixed finite element methods / 79 Overlapping additive Schwarz preconditioners for elliptic PDEs… (More)

- P A Farrell, J J H Miller, E O 'riordan, G I Shishkin
- 1998

In this paper a singularly perturbed reaction-diffusion equation with a dis-continuous source term is examined. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented which… (More)

- P A Farrell, A F Hegarty, J J H Miller, E O 'riordan, G I Shishkin
- 2001

In this paper a singularly perturbed convection–diffusion equation with a discontinuous source term is examined. Boundary and weak interior layers appear in the solution. A numerical method is constructed for this problem which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular… (More)

- Paul A Farrell, Pieter W Hemker, Grigori I Shishkin, P A Farrell, P W Hemker, G I Shishkin
- 1996

In his series of three papers we study singularly perturbed (SP) boundary value problems for equations of elliptic and parabolic type. For small values of the perturbation parameter parabolic boundary and interior layers appear in these problems. If classical discretisation methods are used, the solution of the nite diierence scheme and the approximation of… (More)

- Paul A Farrell, Pieter W Hemker, Grigori I Shishkin, P A Farrell, P W Hemker, G I Shishkin
- 1995

In his series of three papers we study singularly perturbed SP boundary value problems for equations of elliptic and parabolic type. For small values of the perturbation parameter parabolic boundary and interior layers appear in these problems. If classical discretisation methods are used, the solution of the nite diierence scheme and the approximation of… (More)

- P A Farrell, A F Hegarty, J J H Miller, E O 'riordan, G I Shishkin
- 1991

In this article we consider grid approximations of a boundary value problem for boundary layer equations for a at plate outside of a neighbourhood of its leading edge. The perturbation parameter " = Re ?1 multiplying the highest derivative can take arbitrary values from the half-interval (0; 1]; here Re is the Reynolds number. We consider the case when the… (More)

BACKGROUND
Prepubescent children may oxidize fatty acids more readily than adults. Therefore, dietary fat needs would be higher for children compared with adults. The dietary fat recommendations are higher for children 4 to 18 yrs (i.e., 25 to 35% of energy) compared with adults (i.e., 20 to 35% of energy). Despite this, many parents and children restrict… (More)

- P A Farrell, A F Hegarty, J J H Miller, E O 'riordan, G I Shishkin
- 1999

The derivatives of the solution of singularly perturbed diierential equations become unbounded as the singular perturbation parameter " tends to zero. Therefore to approximate such derivatives, it is required to scale the derivatives in such a way that they are of order one for all values of the perturbation parameter. In practice , derivatives are related… (More)

Vascular complications associated with diabetes mellitus (DM) have been linked to activation of PKC-dependent signaling pathways in both human and animal models of DM. To determine whether aberrant PKC signaling mechanisms specifically impact the coronary circulation, we assessed isolated coronary artery (CA) responses after the induction of Type 1 DM. Male… (More)

- P A Farrell, A F Hegarty, J J H Miller, E O 'riordan, G I Shishkin
- 2000

In this paper we describe an experimental technique for computing realistic values of the parameter–uniform order of convergence and error constant in the maximum norm associated with a parameter–uniform numerical method for solving singularly perturbed problems. We employ the technique to compute Reynolds– uniform error bounds in the maximum norm for the… (More)