{"id":{"repo_id":"cadiz","oai_identifier":"oai:rodin.uca.es:10498/32685"},"canonical_url":"https://search.dev.ndltd.org/etd/cadiz/oai:rodin.uca.es:10498/32685","repository":{"repo_id":"cadiz","name":"Universidad de Cadiz","base_url":"https://rodin.uca.es/oai/request"},"display":{"title":"Analysis and numerical simulation of tumor growth models","abstract":"In this dissertation we focus on the numerical analysis of tumor growth models. Due to the difficulty of developing physically meaningful approximations of such models, we divide the main problem into more simple pieces of work that are addressed in the different chapters. First, in Chapter 2 we present a new upwind discontinuous Galerkin (DG) scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the pointwise bounds and prevents non-physical spurious oscillations. These ideas are based on a well-suited piecewise constant approximation of convection equations. The proposed numerical scheme is contrasted with other approaches in several numerical experiments. Afterwards, in Chapter 3, we extend the previous ideas to a mass-conservative, positive and energy-dissipative approximation of the Keller Segel model for chemotaxis. Then we carry out several numerical tests in regimes of chemotactic collapse. These ideas are used later in Chapter 4 to develop a well-suited approximation of two different models related to chemotaxis: a generalization of the classical Keller-Segel model and a model of the neuroblast migration process to the olfactory bulb in rodents brains. Now we propose and study a phase-field tumor growth model in Chapter 5. Then, we develop an upwind DG scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model and we show both the good properties of the approximation and the qualitative behavior of the model in several numerical tests. Next, in Chapter 6, we present two new coupled and decoupled approximations of a Cahn Hilliard Navier Stokes model with variable densities and degenerate mobility that preserve the physical properties of the model. Both approaches are compared in different computational tests including benchmark problems. Consequently, we propose, in Chapter 7, an extension of the previous tumor model including the effects of the surrounding fluid by means of a Cahn Hilliard Darcy model for which obtaining a physically meaningful approximation seems rather plausible using the previous ideas. Finally, this and other future lines of research are described, along with the conclusions and the scientific production of the dissertation, in Chapter 8.","abstract_html":"In this dissertation we focus on the numerical analysis of tumor growth models. Due to the difficulty of developing physically meaningful approximations of such models, we divide the main problem into more simple pieces of work that are addressed in the different chapters. First, in Chapter 2 we present a new upwind discontinuous Galerkin (DG) scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the pointwise bounds and prevents non-physical spurious oscillations. These ideas are based on a well-suited piecewise constant approximation of convection equations. The proposed numerical scheme is contrasted with other approaches in several numerical experiments. Afterwards, in Chapter 3, we extend the previous ideas to a mass-conservative, positive and energy-dissipative approximation of the Keller Segel model for chemotaxis. Then we carry out several numerical tests in regimes of chemotactic collapse. These ideas are used later in Chapter 4 to develop a well-suited approximation of two different models related to chemotaxis: a generalization of the classical Keller-Segel model and a model of the neuroblast migration process to the olfactory bulb in rodents brains. Now we propose and study a phase-field tumor growth model in Chapter 5. Then, we develop an upwind DG scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model and we show both the good properties of the approximation and the qualitative behavior of the model in several numerical tests. Next, in Chapter 6, we present two new coupled and decoupled approximations of a Cahn Hilliard Navier Stokes model with variable densities and degenerate mobility that preserve the physical properties of the model. Both approaches are compared in different computational tests including benchmark problems. Consequently, we propose, in Chapter 7, an extension of the previous tumor model including the effects of the surrounding fluid by means of a Cahn Hilliard Darcy model for which obtaining a physically meaningful approximation seems rather plausible using the previous ideas. Finally, this and other future lines of research are described, along with the conclusions and the scientific production of the dissertation, in Chapter 8.","abstract_has_math":false,"creators":["Acosta Soba, Daniel"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Rodríguez Galván, José Rafael","Wang, Jin","Guillén González, Francisco"],"committee_chairs":[],"committee_members":[],"year":2024,"date_issued":"2024-03-08","date_published":"2024-03-08","updated_at":"2026-07-24T01:29:24Z","subjects":[],"languages":["eng"],"rights":["Attribution-NonCommercial-NoDerivatives 4.0 Internacional"],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10498/32685","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rodríguez Galván, José Rafael","Wang, Jin","Guillén González, Francisco"]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Matemáticas"]},{"key":"dc:creator","label":"Author","values":["Acosta Soba, Daniel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2024-06-20T15:34:01Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-06-20T15:34:01Z"]},{"key":"dc:date.issued","label":"Date","values":["2024-03-08"]},{"key":"dc:type","label":"Dc Type","values":["doctoral thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Attribution-NonCommercial-NoDerivatives 4.0 Internacional"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://creativecommons.org/licenses/by-nc-nd/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10498/32685"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this dissertation we focus on the numerical analysis of tumor growth models. Due to the difficulty of developing physically meaningful approximations of such models, we divide the main problem into more simple pieces of work that are addressed in the different chapters. First, in Chapter 2 we present a new upwind discontinuous Galerkin (DG) scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the pointwise bounds and prevents non-physical spurious oscillations. These ideas are based on a well-suited piecewise constant approximation of convection equations. The proposed numerical scheme is contrasted with other approaches in several numerical experiments. Afterwards, in Chapter 3, we extend the previous ideas to a mass-conservative, positive and energy-dissipative approximation of the Keller Segel model for chemotaxis. Then we carry out several numerical tests in regimes of chemotactic collapse. These ideas are used later in Chapter 4 to develop a well-suited approximation of two different models related to chemotaxis: a generalization of the classical Keller-Segel model and a model of the neuroblast migration process to the olfactory bulb in rodents brains. Now we propose and study a phase-field tumor growth model in Chapter 5. Then, we develop an upwind DG scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model and we show both the good properties of the approximation and the qualitative behavior of the model in several numerical tests. Next, in Chapter 6, we present two new coupled and decoupled approximations of a Cahn Hilliard Navier Stokes model with variable densities and degenerate mobility that preserve the physical properties of the model. Both approaches are compared in different computational tests including benchmark problems. Consequently, we propose, in Chapter 7, an extension of the previous tumor model including the effects of the surrounding fluid by means of a Cahn Hilliard Darcy model for which obtaining a physically meaningful approximation seems rather plausible using the previous ideas. Finally, this and other future lines of research are described, along with the conclusions and the scientific production of the dissertation, in Chapter 8."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Analysis and numerical simulation of tumor growth models"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rodríguez Galván, José Rafael","Wang, Jin","Guillén González, Francisco"],"dc:contributor.other":["Matemáticas"],"dc:creator":["Acosta Soba, Daniel"],"dc:date.accessioned":["2024-06-20T15:34:01Z"],"dc:date.available":["2024-06-20T15:34:01Z"],"dc:date.issued":["2024-03-08"],"dc:description.abstract":["In this dissertation we focus on the numerical analysis of tumor growth models. Due to the difficulty of developing physically meaningful approximations of such models, we divide the main problem into more simple pieces of work that are addressed in the different chapters. First, in Chapter 2 we present a new upwind discontinuous Galerkin (DG) scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the pointwise bounds and prevents non-physical spurious oscillations. These ideas are based on a well-suited piecewise constant approximation of convection equations. The proposed numerical scheme is contrasted with other approaches in several numerical experiments. Afterwards, in Chapter 3, we extend the previous ideas to a mass-conservative, positive and energy-dissipative approximation of the Keller Segel model for chemotaxis. Then we carry out several numerical tests in regimes of chemotactic collapse. These ideas are used later in Chapter 4 to develop a well-suited approximation of two different models related to chemotaxis: a generalization of the classical Keller-Segel model and a model of the neuroblast migration process to the olfactory bulb in rodents brains. Now we propose and study a phase-field tumor growth model in Chapter 5. Then, we develop an upwind DG scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model and we show both the good properties of the approximation and the qualitative behavior of the model in several numerical tests. Next, in Chapter 6, we present two new coupled and decoupled approximations of a Cahn Hilliard Navier Stokes model with variable densities and degenerate mobility that preserve the physical properties of the model. Both approaches are compared in different computational tests including benchmark problems. Consequently, we propose, in Chapter 7, an extension of the previous tumor model including the effects of the surrounding fluid by means of a Cahn Hilliard Darcy model for which obtaining a physically meaningful approximation seems rather plausible using the previous ideas. Finally, this and other future lines of research are described, along with the conclusions and the scientific production of the dissertation, in Chapter 8."],"dc:format":["application/pdf"],"dc:identifier.uri":["http://hdl.handle.net/10498/32685"],"dc:language.iso":["eng"],"dc:rights":["Attribution-NonCommercial-NoDerivatives 4.0 Internacional"],"dc:rights.uri":["http://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:title":["Analysis and numerical simulation of tumor growth models"],"dc:type":["doctoral thesis"]},"updated_at":"2026-07-24T01:29:24Z"}