SelectedWorks - Jeffrey S. Ovall

Contact

Selected Works of Jeffrey S. Ovall

Maseeh Professor, Fariborz Maseeh Department of Mathematics and Statistics

Jeffrey S. Ovall is a Maseeh Professor at the Fariborz Maseeh Department of Mathmematics and Statistics, Portland State University. His area of speciality is Numerical Analysis and Scientific Computation for Partial Differential Equations and Integral Equations, with emphases on Eigenvalue Problems and A Posteriori Error Estimation.

Works
About

×

About Jeffrey S. Ovall

Jeffrey S. Ovall is a Maseeh Professor at the Fariborz Maseeh Department of Mathmematics and Statistics, Portland State University. His area of speciality is Numerical Analysis and Scientific Computation for Partial Differential Equations and Integral Equations, with emphases on Eigenvalue Problems and A Posteriori Error Estimation.

Present	Associate Professor, Portland State University ‐ Fariborz Maseeh Department of Mathematics and Statistics
Institution Organization Position Type Position Title Time Period to Options Current Position Affiliate my profile with this Institution

Cancel

Mathematics and Statistics and Probability

Numerical analysis, Scientific computation, and Partial differential equations

Advanced Numerical Analysis (651)

Faculty Home Page

http://orcid.org/0000-0003-1944-2872

Articles (31)

Korn's Inequality and Eigenproblems for the Lame Operator

Computational Methods in Applied Mathematics (2022)

Sebastian A. Dominguez-Rivera, Nilima Nigam and Jeffrey S. Ovall

In this paper, we show that the so-called Korn inequality holds for vector fields with a zero normal or tangential ...

An Algorithm for Identifying Eigenvectors Exhibiting Strong Spatial Localization

Jeffrey S. Ovall and Robyn Reid

We introduce an approach for exploring eigenvector localization phenomena for a class of (unbounded) selfadjoint operators. More specifically, given a ...

Quadrature for Implicitly-Defined Finite Element Functions on Curvilinear Polygons

Computers & Mathematics with Applications (2022)

Jeffrey S. Ovall and Samuel E Reynolds

Abstract H1" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; line-height: normal; font-size: 16.2px; word-spacing: normal; overflow-wrap: normal; white-space: ...

A Posteriori Error Estimates for Elliptic Eigenvalue Problems Using Auxiliary ...

Mathematics and Statistics Faculty Publications and Presentations (2020)

Stefano Giani, Luka Grubišić, Harri Hakula and Jeffrey S. Ovall

We propose an a posteriori error estimator for high-order p- or hp-finite element discretizations of selfadjoint linear elliptic eigenvalue problems ...

Spectral Discretization Errors in Filtered Subspace Iteration

Mathematics of Computation (2020)

Jeffrey S. Ovall

We consider filtered subspace iteration for approximating a cluster of eigenvalues (and its associated eigenspace) of a (possibly unbounded) selfadjoint ...

Trefftz Finite Elements on Curvilinear Polygons

SIAM Journal on Scientific Computing (2020)

Jeffrey S. Ovall

We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral ...

Analysis of FEAST Spectral Approximations Using the DPG Discretization

Computational Methods in Applied Mathematics (2019)

Jeffrey S. Ovall

A filtered subspace iteration for computing a cluster of eigenvalues and its accompanying eigenspace, known as “FEAST”, has gained considerable ...

A Nyström-based finite element method on polygonal elements

Computers and Mathematics with Applications (2018)

Jeffrey S. Ovall

We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of ...

A high-order method for evaluating derivatives of harmonic functions in ...

SIAM Journal on Scientific Computing (2018)

Jeffrey S. Ovall

We propose a high-order integral equation based method for evaluating interior and boundary derivatives of harmonic functions that are specified ...

An a posteriori estimator of eigenvalue/eigenvector error for penalty-type ...

Applied Mathematics and Computation (2018)

Jeffrey S. Ovall

We provide an abstract framework for analyzing discretization error for eigenvalue problems discretized by discontinuous Galerkin methods such as the ...

A Posteriori Estimates Using Auxiliary Subspace Techniques

Journal of Scientific Computing (2017)

Jeffrey S. Ovall

A posteriori error estimators based on auxiliary subspace techniques for second order elliptic problems in Rd (d ≥ 2) are ...

Some Remarks on Interpolation and Best Approximation

Numerische Mathematik (2017)

Jeffrey S. Ovall

Sufficient conditions are provided for establishing equivalence between best approximation error and projection/interpolation error in finite-dimensional vector spaces for general ...

Benchmark results for testing adaptive finite element eigenvalue procedures part ...

Applied Numerical Mathematics (2016)

Jeffrey S. Ovall

We present an hp-adaptive continuous Galerkin (hp-CG) method for approximating eigenvalues of elliptic operators, and demonstrate its utility on a ...

Robust error estimates for approximations of non-self-adjoint eigenvalue problems

Numerische Mathematik (2016)

Jeffrey S. Ovall

We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection– ...

The Laplacian and Mean and Extreme Values

The American Mathematical Monthly (2016)

Jeffrey S. Ovall

The Laplace operator is pervasive in many important mathematical models, and fundamental results such as the mean value theorem for ...

A posteriori eigenvalue error estimation for a Schrodinger operator with ...

Discrete and Continuous Dynamical Systems Series B (2015)

Jeffrey S. Ovall

We develop an a posteriori error estimate of hierarchical type for Dirichlet eigenvalue problems of the form (−∆ + (c/r)2)ψ ...

A posteriori error estimation of hierarchical type for the Schro ...

Numerische Mathematik (2014)

Jeffrey S. Ovall

We develop an a posteriori error estimate for mixed boundary value problems of the form (−\Delta + V )u = ...

Error control for hp-adaptive approximations of semi-definite eigenvalue problems

Computing (2013)

Jeffrey S. Ovall

We present reliable α-posteriori error estimates for hp-adaptive finite element approximations of semi-definite eigenvalue/eigenvector problems. Our model problems are motivated ...

Rapid error reduction for block Gauss–Seidel based on p-hierarchical ...

Numerical Linear Algebra with Applications (2013)

Jeffrey S. Ovall

We consider a two-level block Gauss–Seidel iteration for solving systems arising from finite element discretizations employing higher-order elements. A p-hierarchical ...

A Framework for Robust Eigenvalue and Eigenvector Error Estimation and ...

Applied Numerical Mathematics (2012)

Jeffrey S. Ovall

We present a general framework for the a posteriori estimation and enhancement of error in eigenvalue/eigenvector computations for symmetric and ...

Benchmark results for testing adaptive finite element eigenvalue procedures

Applied Numerical Mathematics (2012)

Jeffrey S. Ovall

A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue ...

Well Conditioned Boundary Integral Equations for Two-Dimensional Sound-Hard Scattering Problems ...

Journal of Integral Equations and Applications (2012)

Jeffrey S. Ovall

We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with ...

A parallel goal-oriented adaptive finite element method for 2.5-D ...

Geophysical Journal International (2011)

Jeffrey S. Ovall

We present a parallel goal-oriented adaptive finite element method that can be used to rapidly compute highly accurate solutions for ...

An efficient, reliable and robust error estimator for elliptic problems ...

Applied Numerical Mathematics (2011)

Jeffrey S. Ovall

An efficient, reliable and robust error estimator for elliptic problems in R^3

A high-order integral algorithm for highly singular PDE solutions in ...

Computing (2009)

Jeffrey S. Ovall

We present a new algorithm, based on integral equation formulations, for the solution of constant-coefficient elliptic partial differential equations (PDE) ...