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A finite element method for second order nonvariational elliptic problems

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posted on 2023-06-08, 15:50 authored by Omar LakkisOmar Lakkis, Tristan Pryer
We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements and applied directly to the nonvariational (nondivergence) form of a second order linear elliptic problem. The key tools are an appropriate concept of “finite element Hessian” and a Schur com- plement approach to solving the resulting linear algebra problem. The method is illustrated with computational experiments on three linear and one quasi-linear PDE, all in nonvariational form.

History

Publication status

  • Published

File Version

  • Published version

Journal

SIAM Journal on Scientific Computing

ISSN

1064-8275

Publisher

Society for Industrial and Applied Mathematics

Issue

2

Volume

33

Page range

786-801

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-09-19

First Open Access (FOA) Date

2013-09-19

First Compliant Deposit (FCD) Date

2013-09-18

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