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Award ID contains: 2110781

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  1. ; (, Journal of Scientific Computing)
    Abstract In this paper we study hybridized discontinuous Galerkin methods for viscoacoustic wave equations with a general number of viscosity terms. For viscoacoustic equations rewritten as a first order symmetric hyperbolic system, we develop a hybridized local discontinuous Galerkin method which is robust for the number of viscosity terms. We show that the method satisfies a discrete energy estimate such that the implicit constants in the energy estimate are independent of the number of viscosity terms and the length of simulation time. Furthermore, we show that the sizes of reduced system after static condensation are independent of the number of viscosity terms. Optimal a priori error estimates with the Crank–Nicolson scheme are proved and numerical test results are included. 
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  2. ; ; ; (, Computers mathematics with applications)
    We introduce and analyze a coupled hybridizable discontinuous Galerkin/discontinuous Galerkin (HDG/DG) method for porous media in which we allow fully and partly immersed faults, and faults that separate the domain into two disjoint subdomains. We prove well-posedness and present an a priori error analysis of the discretization. Numerical examples verify our analysis. 
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    Free, publicly-accessible full text available December 15, 2026
  3. (, Computers and mathematics with applications)
    In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott-Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included. 
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    Free, publicly-accessible full text available November 15, 2025
  4. ; ; ; (, Computers & Mathematics with Applications)
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  5. ; ; (, ESAIM: Mathematical Modelling and Numerical Analysis)
    In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier–Stokes equations coupled to the quasi-static poroelasticity equationsviainterface conditions. We determine a bound on the data that guarantees stability and well-posedness of the fully discrete problem and provea priorierror estimates. A numerical example confirms our analysis. 
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  6. ; (, Journal of Computational and Applied Mathematics)
    We develop mixed finite element methods for nonlinear reaction–diffusion equations with interfaces which have Robin-type interface conditions. We introduce the velocity of chemicals as new variables and reformulate the governing equations. The stability of semidiscrete solutions, existence and the a priori error estimates of fully discrete solutions are proved by fixed point theorem and continuous/discrete Gronwall inequalities. Numerical results illustrating our theoretical analysis are included. 
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  7. ; ; (, ESAIM: Mathematical Modelling and Numerical Analysis)
    We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier–Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimala priorierror analysis for the fully discrete problem when using Backward Euler time stepping. The theoretical results are verified by numerical examples. 
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  8. ; (, Computers & Mathematics with Applications)
    In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results. 
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  9. ; ; (, Journal of Scientific Computing)
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  10. ; ; (, Computers & Mathematics with Applications)
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