Mats G. Larson

Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method

We propose and analyze a discontinuous finite element method for nearly incompressible linear elasticity on triangular meshes. We show optimal error estimates that are uniform with respect to Poissons ratio. The method is thus locking free. We also introduce an equivalent mixed formulation, allowing for completely incompressible elasticity problems. Numerical results are presented.

Energy norm a posteriori error estimation for discontinuous Galerkin methods

In this paper we present a residual-based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous Galerkin approximations of elliptic problems. The theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed. We also present some illustrating numerical examples.

Analysis of a family of discontinuous Galerkin methods for elliptic problems: the one dimensional case

Summary.In this paper we analyze a family of discontinuous Galerkin methods, parameterized by two real parameters, for elliptic problems in one dimension. Our main results are: (1) a complete inf-sup stability analysis characterizing the parameter values yielding a stable scheme and energy norm error estimates as a direct consequence thereof, (2) an analysis of the error in L2 where the standard duality argument only works for special parameter values yielding a symmetric bilinear form and different orders of convergence are obtained for odd and even order polynomials in the nonsymmetric case. The analysis is consistent with numerical results and similar behavior is observed in two dimensions.

Analysis of a Nonsymmetric Discontinuous Galerkin Method for Elliptic Problems: Stability and Energy Error Estimates

In this paper we analyze a nonsymmetric discontinuous Galerkin method for elliptic problems proposed by Oden, Babuska, and Baumann. Our main results are a complete inf-sup stability analysis and, as a consequence, error estimates in a mesh dependent energy norm allowing variable meshsize and order of polynomials. The analysis is carried out in two spatial dimensions on an unstructured triangulation.

Adaptive multilevel finite element approximations of semilinear elliptic boundary value problems

Summary. In this paper we consider two aspects of the problem of designing efficient numerical methods for the approximation of semilinear boundary value problems. First we consider the use of two and multilevel algorithms for approximating the discrete solution. Secondly we consider adaptive mesh refinement based on feedback information from coarse level approximations. The algorithms are based on an a posteriori error estimate, where the error is estimated in terms of computable quantities only. The a posteriori error estimate is used for choosing appropriate spaces in the multilevel algorithms, mesh refinements, as a stopping criterion and finally it gives an estimate of the total error.

A P2-continuous, P1-discontinuous finite element method for the Mindlin-Reissner plate model

We present a discontinuous finite element method for the Mindlin-Reissner plate model based on continuous piecewise second degree polynomials for the transverse displacements and discontinuous piecewise linear approximations for the rotations. We prove convergence, uniformly in the thickness of the plate, and thus show that locking is avoided. Lastly, we present numerical results.