A posteriori estimates for the stationary Stokes problem in exterior domains

This paper is concerned with the analysis of the inf-sup condition arising in the stationary Stokes problem in exterior domains and applications to the derivation of computable bounds for the distance between the exact solution of the exterior Stokes problem and a certain approximation (which may be of a rather general form). In the first part, guaranteed bounds are deduced for the constant in the stability lemma associated with the exterior domain. These bounds depend only on known constants and the stability constant related to bounded domains that arise after suitable truncations of the unbounded domains. The lemma in question implies computable estimates of the distance to the set of di…

Functional a posteriori error equalities for conforming mixed approximations of elliptic problems

Functional a posteriori error estimates for boundary element methods

Functional error estimates are well-established tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM and the collocation method, what makes the approach of particular interest for scientific computations and engineering applications. Numerical experiments for the Laplace problem confirm the theoretical results.

Generalized Maxwell equations in exterior domains 3, Electro-magneto statics

Functional A Posteriori Error Equalities for Conforming Mixed Approximations of Elliptic Problems

In this paper we show how to find the exact error (not just an estimate of the error) of a conforming mixed approximation by using the functional type a posteriori error estimates in the spirit of Repin. The error is measured in a mixed norm which takes into account both the primal and dual variables. We derive this result for elliptic partial differential equations of a certain class. We first derive a special version of our main result by using a simplified reaction-diffusion problem to demonstrate the strong connection to the classical functional a posteriori error estimates of Repin. After this we derive the main result in an abstract setting. Our main result states that in order to obt…

Generalized Maxwell equations in exterior domains 1, Regularity results, trace theorems and static solution theory

Generalized Maxwell equations in exterior domains 2, Radiation problems and low frequency behavior

Computation of generalized time-periodic waves using differential forms, exact controllability, least-squares formulation, conjugate gradient method and discrete exterior calculus Part 1, Theoretical considerations

Generalized Maxwell equations in exterior domains 4, Hodge-Helmholtz decompositions

Generalized Maxwell equations in exterior domains 5, Low frequency asymptotics