Publication

MATHICSE Technical Report : Analysis of the internodes method for non-conforming discretizations of elliptic equations

Alfio Quarteroni
2016
Working Papers

Abstract

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interface, the others for the Neumann trace. In this paper we provide several interpretations of the method and we carry out its stability and convergence analysis. In every subdomain the original problem is discretized by the finite element method, using a priori non-matching grids and piecewise polynomials of different degree. Finally, we propose an efficient algorithm for the solution of the corresponding algebraic system.

Official source

https://infoscience.epfl.ch/entities/publication/2826f1cb-169b-49a5-9469-476e655a949e

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Alfio Quarteroni
2016
Working Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/2826f1cb-169b-49a5-9469-476e655a949e

About this result

Related concepts (32)

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

Elliptic partial differential equation

Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form where A, B, C, D, E, F, and G are functions of x and y and where , and similarly for . A PDE written in this form is elliptic if with this naming convention inspired by the equation for a planar ellipse.

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MATHICSE Technical Report : Analysis of the internodes method for non-conforming discretizations of elliptic equations

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