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- By A. H. Schatz, L. B. Wahlbin
- 2010

Interior a priori error estimates in the maximum norm are derived from interior Ritz-Galerkin equations which are common to a class of methods used in approximating solutions of second order elliptic boundary value problems. The estimates are valid for a large class of piecewise polynomial subspaces used in practice, which are defined on quasi-uniform… (More)

For a model convection-dominated singularly perturbed convection-diffusion problem, it is shown that crosswind smear in the numerical streamline diffusion finite element method is minimized by introducing a judicious amount of artificial crosswind diffusion. The ensuing method with piecewise linear elements converges with a pointwise accuracy of almost hi/A… (More)

- Lars B. Wahlbin
- SIAM Review
- 1992

- Stig Larsson, Vidar Thomée, Lars B. Wahlbin
- Math. Comput.
- 1998

The numerical solution of a parabolic equation with memory is considered. The equation is first discretized in time by means of the discontinuous Galerkin method with piecewise constant or piecewise linear approximating functions. The analysis presented allows variable time steps which, as will be shown, can then efficiently be selected to match… (More)

The finite element method is considered when applied to a model Dirichlet problem on a plane polygonal domain. Rate of convergence estimates in the maximum norm, up to the boundary, are given locally. The rate of convergence may vary from point to point and is shown to depend on the local smoothness of the solution and on a possible pollution effect. In one… (More)

- Wolfgang Hoffmann, Alfred H. Schatz, Lars B. Wahlbin, Gabriel Wittum
- Math. Comput.
- 2001

A class of a posteriori estimators is studied for the error in the maximum-norm of the gradient on single elements when the finite element method is used to approximate solutions of second order elliptic problems. The meshes are unstructured and, in particular, it is not assumed that there are any known superconvergent points. The estimators are based on… (More)

Second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered. The behavior of the ordinary Galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed.

- Vidar Thomée, Lars B. Wahlbin
- Numerische Mathematik
- 2000

- Ricardo H. Nochetto, Lars B. Wahlbin
- Math. Comput.
- 2002

We consider finite element operators defined on “rough” functions in a bounded polyhedron Ω in RN . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of Ω and approximating general functions which do not. We give impossibility results for… (More)

Error estimates of optimal order are proved for semidiscreteand completely discrete nite element methods for a linear wave equation with strong damping, arising in viscoelastic theory. It is demonstrated that the exact solution may be interpreted in terms of an analyticsemigroup, and as a result that, althoughthe solution has essentially the spatial… (More)