Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

F. A. Milner, Eun-Jae Park

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.

Original languageEnglish
Pages (from-to)399-412
Number of pages14
JournalIMA Journal of Numerical Analysis
Volume16
Issue number3
DOIs
Publication statusPublished - 1996 Jan 1

Fingerprint

Optimal Error Estimates
Hamilton-Jacobi
Mixed Finite Element Method
Elliptic Operator
Dirichlet Problem
Error Estimates
Divergence
Existence and Uniqueness
Numerical Solution
Nonlinearity
Finite element method
Zero
Arbitrary
Term
Approximation
Form

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

@article{47c36552b91e47ca8e9e706d52d8bf2b,
title = "Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations",
abstract = "The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.",
author = "Milner, {F. A.} and Eun-Jae Park",
year = "1996",
month = "1",
day = "1",
doi = "10.1093/imanum/16.3.399",
language = "English",
volume = "16",
pages = "399--412",
journal = "IMA Journal of Numerical Analysis",
issn = "0272-4979",
publisher = "Oxford University Press",
number = "3",

}

Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations. / Milner, F. A.; Park, Eun-Jae.

In: IMA Journal of Numerical Analysis, Vol. 16, No. 3, 01.01.1996, p. 399-412.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Mixed finite-element methods for Hamilton-Jacobi-Bellman-type equations

AU - Milner, F. A.

AU - Park, Eun-Jae

PY - 1996/1/1

Y1 - 1996/1/1

N2 - The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.

AB - The numerical solution of Dirichlet's problem for a second-order elliptic operator in divergence form with arbitrary nonlinearities in the first-and zero-order terms is considered. The mixed finite-element method is used. Existence and uniqueness of the approximation are proved and optimal error estimates in L2 are demonstrated for the relevant functions. Error estimates are also derived in Lq, 2 ≤ q ≤ + ∞.

UR - http://www.scopus.com/inward/record.url?scp=0030486473&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030486473&partnerID=8YFLogxK

U2 - 10.1093/imanum/16.3.399

DO - 10.1093/imanum/16.3.399

M3 - Article

AN - SCOPUS:0030486473

VL - 16

SP - 399

EP - 412

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

SN - 0272-4979

IS - 3

ER -