Immanuel Anjam

A posteriori error estimates for a Maxwell type problem

Abstract In this paper, we discuss a posteriori estimates for the Maxwell type boundary-value problem. The estimates are derived by transformations of integral identities that define the generalized solution and are valid for any conforming approximation of the exact solution. It is proved analytically and confirmed numerically that the estimates indeed provide a computable and guaranteed bound of approximation errors. Also, it is shown that the estimates imply robust error indicators that represent the distribution of local (inter-element) errors measured in terms of different norms.

Fast MATLAB assembly of FEM matrices in 2D and 3D

We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H ( div ) spaces and Nedelec elements in discretizations of H ( curl ) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.

A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries ∗

We present an algorithm for two- and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algorithm decreases with better resolution of the input image. Those features render the presented algorithm well suited for fast prototyping while using the most realistic IC geometry data.

On a posteriori error bounds for approximations of the generalized Stokes problem generated by the Uzawa algorithm

Abstract In this paper, we derive computable a posteriori error bounds for approximations computed by the Uzawa algorithm for the generalized Stokes problem. We show that for each Uzawa iteration both the velocity error and the pressure error are bounded from above by a constant multiplied by the L2-norm of the divergence of the velocity. The derivation of the estimates essentially uses a posteriori estimates of the functional type for the Stokes problem.

An Elementary Method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations

Abstract In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal and dual variables. We work only on the continuous (often called functional) level and do not suppose any specific properties of numerical methods and discretizations.

Functional A Posteriori Error Control for Conforming Mixed Approximationsof Coercive Problems with Lower Order Terms

Abstract The results of this contribution are derived in the framework of functional type a posteriori error estimates. The error is measured in a combined norm which takes into account both the primal and dual variables denoted by x and y, respectively. Our first main result is an error equality for all equations of the class A * ⁢ A ⁢ x + x = f

On the Reliability of Error Indication Methods for Problems with Uncertain Data

{\mathrm{A}^{*}\mathrm{A}x+x=f}

A Unified Approach to Measuring Accuracy of Error Indicators

or in mixed formulation A * ⁢ y + x = f

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

{\mathrm{A}^{*}y+x=f}

A posteriori error control for Maxwell and elliptic type problems

, A ⁢ x = y