An optimal triangulation for second-order elliptic problems

Least Squares for Second Order Elliptic Problems

In this paper we introduce and analyze two least squares methods for second order elliptic di erential equations with mixed boundary conditions These methods extend to problems which involve oblique derivative boundary conditions as well as nonsym metric and inde nite problems as long as the original problem has a unique solution With the methods to be developed Neumann and oblique boundary con...

Low Order Discontinuous Galerkin Methods for Second Order Elliptic Problems

Abstract. We consider DG-methods for 2nd order scalar elliptic problems using piecewise affine approximation in two or three space dimensions. We prove that both the symmetric and the nonsymmetric version of the DG-method are well-posed also without penalization of the interelement solution jumps provided boundary conditions are imposed weakly. Optimal convergence is proved for sufficiently reg...

Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems

A new approach of constructing algebraic multilevel preconditioners for mixed nite element methods for second order elliptic problems with tensor coe cients on general geometry is proposed The linear system arising from the mixed methods is rst algebraically condensed to a symmetric positive de nite system for Lagrange multipliers which corresponds to a linear system generated by standard nonco...

Optimal Preconditioning for Raviart-Thomas Mixed Formulation of Second-Order Elliptic Problems

Tractability of quasilinear problems II: Second-order elliptic problems

In a previous paper, we developed a general framework for establishing tractability and strong tractability for quasilinear multivariate problems in the worst case setting. One important example of such a problem is the solution of the Helmholtz equation −∆u + qu = f in the d-dimensional unit cube, in which u depends linearly on f , but nonlinearly on q. Here, both f and q are d-variate functio...