An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
An upwind difference scheme on a novel Shishkin-type mesh for a linear convection-diffusion problem
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
MooNMD – a program package based on mapped finite element methods
Computing and Visualization in Science
SIAM Journal on Numerical Analysis
Superconvergence analysis of the SDFEM for elliptic problems with characteristic layers
Applied Numerical Mathematics
Using rectangular Qp elements in the SDFEM for a convection--diffusion problem with a boundary layer
Applied Numerical Mathematics
Applied Numerical Mathematics
Superconvergence using pointwise interpolation in convection-diffusion problems
Applied Numerical Mathematics
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Singularly perturbed convection–diffusion problems with exponential and characteristic layers are considered on the unit square. The discretisation is based on layer-adapted meshes. The standard Galerkin method and the local projection scheme are analysed for bilinear and higher order finite element where enriched spaces were used. For bilinears, first order convergence in the ε-weighted energy norm is shown for both the Galerkin and the stabilised scheme. However, supercloseness results of second order hold for the Galerkin method in the ε-weighted energy norm and for the local projection scheme in the corresponding norm. For the enriched $${\mathcal{Q}_p}$$-elements, p ≥ 2, which already contain the space $${\mathcal{P}_{p+1}}$$, a convergence order p + 1 in the ε-weighted energy norm is proved for both the Galerkin method and the local projection scheme. Furthermore, the local projection methods provides a supercloseness result of order p + 1 in local projection norm.