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In this work we study a residual based a posteriori error estimation for the CutFEM method applied to an elliptic model problem. We consider the problem with non-polygonal boundary and the analysis takes into account the geometry and data approximation on the boundary. The reliability and efficiency are theoretically proved. Moreover, constants are robust with respect to how the domain boundary cuts the mesh.
In this article, we aim to recover locally conservative and $H(div)$ conforming fluxes for the linear Cut Finite Element Solution with Nitsches method for Poisson problems with Dirichlet boundary condition. The computation of the conservative flux in
We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a non-conforming d
This article investigates residual a posteriori error estimates and adaptive mesh refinements for time-dependent boundary element methods for the wave equation. We obtain reliable estimates for Dirichlet and acoustic boundary conditions which hold fo
Finite element exterior calculus (FEEC) has been developed over the past decade as a framework for constructing and analyzing stable and accurate numerical methods for partial differential equations by employing differential complexes. The recent wor
Many practical problems occur due to the boundary value problem. This paper evaluates the finite element solution of the boundary value problem of Poissons equation and proposes a novel a posteriori local error estimation based on the Hypercircle met