Mixed methods for fourth-order elliptic and parabolic problems using radial basis functions
type: Item
instance of: scholarly article
title: Mixed methods for fourth-order elliptic and parabolic problems using radial basis functions
zbMATH Open document ID: 1069.65107
author: Jichun Li
published in: Advances in Computational Mathematics
publication date: 2005-04-28T00:00:00Z
review text: Mixed methods for solving fourth-order elliptic and parabolic problems by using radial basis functions are developed. The author considers the elliptic problem of the form \[ \Delta^2 u+b(\mathbf{x}) u=f(\mathbf{x})\quad \text{in}\;\;\Omega,\quad \frac{\partial u}{\partial\nu}=\frac{\partial \Delta u}{\partial\nu}=0 \quad \text{on}\;\;\partial\Omega, \] where \(\Omega\subset \mathbb{R}^d\;(d\leq 3)\) is an open and bounded domain, having a \(C^1\)-boundary, and the following parabolic problem \[ \begin{gathered} \frac{\partial u}{\partial t}+\Delta^2 u+b(\mathbf{x},t) u=f(\mathbf{x},t)\quad \text{in}\;\;\Omega\times (0,T)\\ \frac{\partial u}{\partial\nu}=\frac{\partial \Delta u}{\partial\nu}=0\quad \text{on}\;\;\partial\Omega\times (0,T),\quad u(\mathbf{x},0)=u_0(\mathbf{x}), \end{gathered} \] where \(b(\mathbf{x},t), (\mathbf{x},t)\in\Omega\times (0,T),\) is a given function. Error estimates are given.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 2162342
zbMATH Keywords: fourth-order elliptic problem
zbMATH Keywords: radial basis functions
zbMATH Keywords: mixed finite element method
zbMATH Keywords: fourth-order parabolic problem
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: s10444-004-1807-7
OpenAlex ID: W2023542601
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DOI: 10.1007/S10444-004-1807-7
description: scientific article; zbMATH DE number 2162342